How do you solve $3^{x} = 500$ $3^x=500$ ?

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Answer 1 · 2018-03-30T16:47:38

$x = \frac{log (500)}{log (3)}$ $x = frac{log(500)}{log(3)}$

First, take the $log$ $log$ of both sides of the equation to get:
$log (3^{x}) = log (500)$ $log(3^{x}) = log(500)$

Then use the logarithmic power property to eliminate the exponent:
$x log (3) = log (500)$ $xlog(3) = log(500)$

Finally, divide both sides of the equation by $log (3)$ $log(3)$ :
$x = \frac{log (500)}{log (3)}$ $x = frac{log(500)}{log(3)}$

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