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How do you solve $5^{x} = 10$ $5^x = 10$ ?

1 Answer

Feb 24, 2016

$x = {log}_{5} 10 \approx 1.430677$ $x=log_5 10 ~~1.430677$

Explanation:

Make use of the standard relationship
$XXX {log}_{b} a = c \Leftrightarrow b^{c} = a$ $color(white)("XXX")log_b a = c <=> b^c = a$
or (reversed)
$XXX b^{c} = a \Leftrightarrow {log}_{b} a$ $color(white)("XXX")b^c=a <=> log_b a$

So
$XXX 5^{x} = 10 \Leftrightarrow {log}_{5} 10 = x$ $color(white)("XXX")5^x= 10 <=> log_5 10 = x$

${log}_{5} 10$ $log_5 10$ can be evaluated using a calculator as $\approx 1.430677$ $~~1.430677$

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