How do you solve $4^{x} = 13$ $4^x=13$ ?

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Answer 1 · 2016-12-30T02:18:13

$x = \frac{ln (13)}{ln (4)} = {log}_{4} (13) \approx 1.850$ $x = ln(13)/ln(4) = log_4(13) ~~ 1.850$

Using the property of logarithms that $log (a^{x}) = x log (a)$ $log(a^x) = xlog(a)$ , we have

$4^{x} = 13$ $4^x = 13$

$\Rightarrow ln (4^{x}) = ln (13)$ $=> ln(4^x) = ln(13)$

$\Rightarrow x ln (4) = ln (13)$ $=> xln(4) = ln(13)$

$:. x = ln(13)/ln(4) = log_4(13) ~~ 1.850$

(The last line uses the fact that $log_a(b) = log(b)/log(a)$ )

How do you solve 4^x=134x=134^x=13?