<ul class="bullet-list"><li data-list-item-id="item-1782714622647-j1zjk4h2k" data-list-item-path="item-1782714622647-j1zjk4h2k"><div class="list-item-paragraph">If both the left and right hand side of the exponential equation equation have one term</div><ol class="abc-list"><li data-list-item-id="subitem-1782714658423-36vk9eqyv" data-list-item-path="item-1782714622647-j1zjk4h2k/subitem-1782714658423-36vk9eqyv"><div class="list-item-paragraph">If both sides of the equation can be prime factorised and expressed as the same base. The exponents are equal</div><div class="list-item-paragraph">\(9^x = 27^2\)<br>\(3^{2x} = 3^6 \)<br>Then&nbsp;\(2x = 6 \rightarrow x = 3\)</div></li><li data-list-item-id="subitem-1782714935140-bwb9p8r65" data-list-item-path="item-1782714622647-j1zjk4h2k/subitem-1782714935140-bwb9p8r65"><div class="list-item-paragraph">If the left and right hand side cannot be expressed as the same base, express the equation in logarithmic form</div><div class="list-item-paragraph">\(2^x = 7\)<br>\(x\lg{2} = \lg{7}\)<br>\(x = \frac{\lg{7}}{\lg{2}} \)</div></li></ol></li><li data-list-item-id="item-1782715701081-5viiscy7l" data-list-item-path="item-1782715701081-5viiscy7l"><div class="list-item-paragraph">Otherwise, if the exponential equation contains more than one term make a suitable substitution to simplify the problem to solving a polynomial</div><div class="list-item-paragraph">\( 3\left(2^x \right)^2 - 4 \left(2^x \right) + 1 = 0\)<br>Let&nbsp;\(2^x = u\)<br>\(3u^2 - 4u + 1 = 0\)<br>\( (u - 3)(u - 1) = 0\)<br>\(u = 3\) or \(u = 1\)<br>\(2^x = 3\) or \(2^x = 1\)<br>\(x = \frac{\lg{3}}{\lg{2}}\) or \(x = 0\)</div></li></ul>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1782718083641-ebt7e97f5v5.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

If both the left and right hand side of the exponential equation equation have one term

Otherwise, if the exponential equation contains more than one term make a suitable substitution to simplify the problem to solving a polynomial

\( 3\left(2^x \right)^2 - 4 \left(2^x \right) + 1 = 0\)
Let \(2^x = u\)
\(3u^2 - 4u + 1 = 0\)
\( (u - 3)(u - 1) = 0\)
\(u = 3\) or \(u = 1\)
\(2^x = 3\) or \(2^x = 1\)
\(x = \frac{\lg{3}}{\lg{2}}\) or \(x = 0\)

Solving Exponential Equations

Solving Exponential Equations