{"id":244845,"date":"2024-06-10T16:00:25","date_gmt":"2024-06-10T08:00:25","guid":{"rendered":"https:\/\/thepiquelab.com\/blog\/?p=244845"},"modified":"2025-06-16T13:23:47","modified_gmt":"2025-06-16T05:23:47","slug":"logarithm-shift-and-push-technique","status":"publish","type":"post","link":"https:\/\/thepiquelab.com\/blog\/logarithm-shift-and-push-technique\/","title":{"rendered":"Logarithm: Using The Shift And Push Technique To Solve Logarithm Equations"},"content":{"rendered":"

[et_pb_section fb_built=”1″ _builder_version=”4.21.0″ global_colors_info=”{}”][et_pb_row _builder_version=”4.21.0″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.16″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_text _builder_version=”4.21.0″ text_font=”||||||||” hover_enabled=”0″ z_index_tablet=”500″ custom_css_main_element=”sub,||sup {||font-size: 75%;||line-height: 0;||position: relative;||vertical-align: baseline;||}||sup {||top: -0.5em;||}||sub {||bottom: -0.25em;||}” global_colors_info=”{}” sticky_enabled=”0″]<\/p>\n

Introduction<\/strong><\/p>\n

Welcome back to another Secondary Math blog post!<\/p>\n

Do you find logarithm equations complicated?<\/p>\n

In today\u2019s blog post, I will teach you how to solve Logarithm<\/strong> equations using the Shift and Push Technique<\/strong> by analysing a question from the 2018 Fuhua Secondary School (FHSS) S3E SA1 Examination Paper<\/strong>.<\/p>\n

Alternatively, you can watch my explainer video on this question here<\/a>.<\/p>\n

\"Click<\/a><\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n\n

Let’s Take A Look At This Logarithm Question<\/span><\/h2>\n

<\/p>\n

<\/p>\n

\"The<\/p>\n

Source: Fuhua Secondary School \u2014 2018 S3E SA1 Examination Paper [Q10(i)]<\/span><\/em>
<\/p>\n

\n

Read Also:<\/h3>\n
    \n
  1. [Secondary 3 A-Math Explainer Video] Logarithm : Solving For Simple Logarithm Equation<\/b><\/a><\/li>\n
  2. Direct Proportion: Finding The Relationship Between Variables\u00a0<\/strong><\/a><\/li>\n<\/ol>\n<\/div>\n

    Thought Process<\/span><\/h2>\n
    \n

    \ud83d\udca1\u00a0What Is A Logarithm Function?<\/strong> \ud83d\udca1<\/p>\n

    A logarithm function, or log function in short, can be rewritten as log\u2090<\/span>x<\/em>.<\/p>\n<\/blockquote>\n

    The a<\/em> term is called the base term, while x<\/em> can represent any expression or certain constant value.<\/p>\n

    \"The<\/p>\n

    \n

    \ud83d\udd0e\u00a0How Can A Logarithm Be Well-Defined?<\/strong> \ud83d\udd0e<\/p>\n

    1\ufe0f\u20e3\u00a0The base term should be positive (a<\/em> > 0).
    2\ufe0f\u20e3\u00a0The base term cannot take up the value of 1 (a<\/em> \u2260 1).
    3\ufe0f\u20e3\u00a0The x<\/em> must always be positive (x<\/em> >0).<\/p>\n<\/blockquote>\n

    If these three conditions are met, the log term is well-defined.<\/p>\n

    Here are some examples of well-defined logarithm functions:<\/p>\n

    \"The<\/p>\n

    But what do these Logarithm Functions really tell us?<\/p>\n

    To answer that, we will call upon the Exponential Function, which can be represented in the form of y=ax<\/sup><\/em>.<\/p>\n

    \"The<\/p>\n

    Do you notice a pattern when you compare each of the corresponding examples?<\/p>\n

    The base terms of 2, 3, and 4, and the numbers 8, 9, and 16 repeat in both functions.<\/p>\n

    \"The<\/p>\n

    However, there is one number that did not repeat on both sides \u2014 the powers of the exponential function. <\/p>\n

    \"The<\/p>\n

    This is exactly what logarithm functions mean. They are the power that the base term will be raised to. Logarithm and exponential functions are related to each other.<\/p>\n

    In our first example, 23<\/sup> gives us 8. Therefore, log\u2082<\/em>8<\/em> will give us 3.<\/p>\n

    In the second line, log\u20839<\/em> will give us 2.<\/p>\n

    What about log\u208416<\/em>? We will get 2!<\/p>\n

    \"The<\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/h2>\n

    Let Us Solve Question 10(i)<\/span>
    <\/h2>\n

    Now that you have a better understanding of what the logarithm function represents, let us go back to Question 10(i) to solve the logarithm equation.<\/p>\n

    \"The<\/span><\/strong><\/p>\n

    Source: Fuhua Secondary School \u2014 2018 S3E SA1 Examination Paper [Q10(i)]<\/span><\/em><\/p>\n

    To solve this equation, we\u2019ll be required to remove the log function.<\/p>\n

    How do we do that?<\/p>\n

    Let us use log\u2082<\/em>8<\/em> as an example. We know that this will be equal to 3 and we can rewrite this as 8=23<\/sup><\/em>.<\/p>\n

    So how do we go about it?<\/p>\n

    First, recall that the 2 in our logarithm function is known as the base term, while the number 3 is known as the power term.<\/p>\n

    To remove logarithm functions, we can use the Shift and Push Technique.<\/p>\n

    \n

    \ud83d\udd03\u00a0What Is The Shift and Push Technique? \ud83d\udd03<\/strong><\/p>\n

    It is a technique used to express any logarithm function in its exponential form.<\/p>\n<\/blockquote>\n

    How does it work?<\/p>\n

    Notice that when we shifted 2 to the other side, it went into the base position. At the same time, it pushes whatever is on the right initially \u2014 in this case the number 3 \u2014 into the power position.<\/p>\n

    \"The<\/p>\n

    Now that you have the idea of how to remove logarithm from an equation, let\u2019s proceed to solve the question.<\/p>\n

    \"The<\/p>\n

    Source: Fuhua Secondary School \u2014 2018 S3E SA1 Examination Paper [Q10(i)]<\/span><\/em><\/p>\n

    In the given equation, x<\/em> plays the role of our base while 2 on the right-hand side plays the role of our power term.<\/p>\n

    We shall remove log from this equation by using the Shift and Push Technique, which removes log to give us this equation:<\/p>\n

    72 – x2 <\/sup><\/em>= x2<\/sup><\/em><\/p>\n

    Now, we can proceed to solve this equation.<\/p>\n

    \"How<\/p>\n

    Because this is a logarithm question, there is one last step that we need to do \u2014 to check if our final answer satisfies the three laws that we discussed earlier.<\/p>\n

    Note that x<\/em> plays the role of the base in the equation. Hence, x<\/em> cannot take up negative values.<\/p>\n

    This means that we have to reject -6, simply because x<\/em> must be positive.<\/p>\n

    Therefore, there is only one final solution.<\/p>\n

    \"How<\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    Suggested Answer<\/span><\/h2>\n

    x<\/em> = 6<\/p>\n

    Conclusion<\/span><\/h2>\n

    I hope that after reading this blog post, you have gained a better understanding of the relationship between the logarithm and exponential functions.<\/p>\n

    Remember to use the Shift and Push Technique to convert any logarithm function to an exponential function!<\/p>\n

    Stay tuned for more Secondary Math tips!<\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

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    In this article, we’ll be discussing how to use the Shift and Push Technique to solve this Secondary 3 A-Math Logarithm question from Fuhua Secondary School.<\/p>\n","protected":false},"author":41,"featured_media":244898,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","om_disable_all_campaigns":false,"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"categories":[66,67],"tags":[],"post_folder":[],"modified_by":"Jaimie Aberia","_links":{"self":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/244845"}],"collection":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/users\/41"}],"replies":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/comments?post=244845"}],"version-history":[{"count":19,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/244845\/revisions"}],"predecessor-version":[{"id":246594,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/244845\/revisions\/246594"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/media\/244898"}],"wp:attachment":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/media?parent=244845"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/categories?post=244845"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/tags?post=244845"},{"taxonomy":"post_folder","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/post_folder?post=244845"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}