How do you solve $3^(2x) = 5$ ?

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Answer 1 · 2016-02-27T19:15:25

$x~~0.73$

$1$ . Notice that the powers on both sides of the equation do not have the same base. Thus, you must log both sides.

$log(3^(2x))=log(5)$

$2$ . Recall the log rule: $log_b(m^color(red)(n))=color(red)(n)log_b(m)$ . Thus, in your equation, bring down the exponent, $2x$ .

$2xlog(3)=log(5)$

$3$ . Solve for $x$ .

$2x=log(5)/log(3)$

$x=log(5)/(2log(3))$

$color(green)(x~~0.73)$

How do you solve 3^(2x) = 53^(2x) = 5?