How do you solve $5^{x} = 28$ $5^x = 28$ ?

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How do you solve $5^{x} = 28$ $5^x = 28$ ?

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Answer 1 · 2016-03-25T02:44:31

$x \approx 2.07$ $x~~2.07$

Explanation:

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

$5^{x} = 28$ $5^x=28$

$log (5^{x}) = log (28)$ $log(5^x)=log(28)$

$2$ $2$ . 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.

$x log (5) = log (28)$ $xlog(5)=log(28)$

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

$x = \frac{log (28)}{log (5)}$ $x=(log(28))/(log(5))$

$color(green)(|bar(ul(color(white)(a/a)x~~2.07color(white)(a/a)|)))$

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How do you solve $5^{x} = 28$ $5^x = 28$ ?

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Explanation:

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