How do you solve $4^ { 8x } = 500$ ?

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Answer 1 · 2017-10-19T16:38:07

One can use any base logarithm that one likes on both sides:

$log_b(4^(8x)) = log_b(500)$

Use the property $log_b(A^C) = (C)log_b(A)$

$(8x)log_b(4) = log_b(500)$

Divide both sides by $8log_b(4)$ :

$x = log_b(500)/(8log_b(4))$

Most calculators have base 10 and base e, therefore, I recommend that you use one of these two bases, for an exact representation of x:

$x = log_10(500)/(8log_10(4)) = ln(500)/(8ln(4))$

Here is an approximate number for x:

$x ~~ 0.560362$

Answer 2 · 2017-10-19T18:56:48

$x = 0.56036$

$4^(8x) = 500$

Taking log on both sides,
$log4^(8x) = log 500$

$8x log 4 = log 500$

$8x = log 500/ log 4 = 2.699 / 0.6021 = 4.4829$

$x = 4.4829/8 ~~ 0.56036$

How do you solve 4^ { 8x } = 5004^ { 8x } = 500?