Question

Solve each equation or inequality. $2 ^ { x - 1 } = 5$

Solution

VerifiedStep 1

1 of 2$2^{x-1}=5$

Take the natural log of both sides

$\ln2^{x-1}=\ln5$

$\text{\color{#c34632}Recall that: $\log_ab^n=n\log_ab$}$

$\left(x-1\right)\ln2=\ln5$

Divide both sides by $\ln2$

$x-1=\dfrac{\ln5}{\ln2}$

$\text{\color{#c34632}Recall that: $\dfrac{\log_cb}{\log_ca}=\log_ab$}$

$x-1=\log_25$

Add 1 on both sides

$x=1+\log_25$

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