How do you solve $4^{x} = 12$ $4^x = 12$ ?

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How do you solve $4^{x} = 12$ $4^x = 12$ ?

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Answer 1 · 2018-03-11T21:05:34

$x = 1.79$ $x=1.79$

Explanation:

Apply the ${log}_{4}$ $log_4$ on both sides of the equation

${log}_{4} (4^{x}) = {log}_{4} (12)$ $log_4(4^x)=log_4(12)$

Apply an Exponent Logarithm Law:
$x \cdot {log}_{4} (4) = {log}_{4} (12)$ $x* log_4(4)=log_4(12)$

${log}_{a} (a)$ $log_a(a)$ always equals 1, so you get:
$x = {log}_{4} (12)$ $x=log_4(12)$

If your calculator doesn't have log bases besides the default (10) you can apply the change of base formula:
$x = \frac{log (12)}{log (4)}$ $x=log(12)/log(4)$

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How do you solve $4^{x} = 12$ $4^x = 12$ ?

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