How do you solve $15^{2 x} = 36$ $15^(2x) = 36$ ?

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How do you solve $15^{2 x} = 36$ $15^(2x) = 36$ ?

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Answer 1 · 2016-03-16T04:26:21

$x \approx 0.66$ $x~~0.66$

Explanation:

$1$ $1$ . Since the left and right sides of the equation do not have the same base, start by taking the log of both sides.

$15^{2 x} = 36$ $15^(2x)=36$

$log (15^{2 x}) = log (36)$ $log(15^(2x))=log(36)$

$2$ $2$ . Use the log property, ${log}_{b} (m^{n}) = n \cdot {log}_{b} (m)$ $log_color(purple)b(color(red)m^color(blue)n)=color(blue)n*log_color(purple)b(color(red)m)$ , to simplify the left side of the equation.

$(2 x) log 15 = log 36$ $(2x)log15=log36$

$3$ $3$ . Solve for $x$ $x$ .

$2 x = \frac{log 36}{log 15}$ $2x=log36/log15$

$x = \frac{log 36}{2 log 15}$ $x=log36/(2log15)$

$color(green)(|bar(ul(color(white)(a/a)x~~0.66color(white)(a/a)|)))$

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How do you solve $15^{2 x} = 36$ $15^(2x) = 36$ ?

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