How do you solve ${log}_{5} 2 x - 5 = - 4$ $log_5 2x − 5 = −4$ ?

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Answer 1 · 2016-05-04T17:39:11

$x = \frac{1563}{625}$ $x=1563/625$

Use definition ${log}_{b} x = y \Leftrightarrow b^{y} = x$ $log_b x=y iff b^y=x$

$5^{- 4} = 2 x - 5$ $5^-4 = 2x-5$

$\frac{1}{5^{4}} = 2 x - 5$ $1/5^4 = 2x-5$

$\frac{1}{625} = 2 x - 5$ $1/625 = 2x-5$

$\frac{1}{625} + 5 = 2 x$ $1/625 + 5 = 2x$

$\frac{3126}{625} = 2 x$ $3126/625 = 2x$

$x = \frac{1563}{625}$ $x=1563/625$

How do you solve log_5 2x − 5 = −4log52x−5=−4log_5 2x − 5 = −4?