How do you solve $2^{x} = 7$ $2^x = 7$ ?

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How do you solve $2^{x} = 7$ $2^x = 7$ ?

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Answer 1 · 2016-03-16T02:10:51

$x \approx 2.81$ $x~~2.81$

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.

$2^{x} = 7$ $2^x=7$

$log (2^{x}) = log (7)$ $log(2^x)=log(7)$

$2$ $2$ . 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 $log (2^{x})$ $log(2^x)$ .

$x log (2) = log (7)$ $xlog(2)=log(7)$

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

$x = \frac{log (7)}{log (2)}$ $x=log(7)/log(2)$

$color(green)(|bar(ul(color(white)(a/a)x~~2.81color(white)(a/a)|)))$

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How do you solve $2^{x} = 7$ $2^x = 7$ ?

1 Answer

Explanation:

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