What is the inverse of log_{10}(y)=5^x ?

The inverse of log_{10}(y)=5^x is (ln(\frac{ln(x))/(ln(10)))}{ln(5)}

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inverse of log_{10}(y)=5^x

inverse

lo g_{10} (y) = 5^{x}

\frac{ln ( \frac{l n ( x )}{l n ( 10 )} )}{ln ( 5 )}

Solution steps

y = 1 0^{5^{x}}

Replace

x

with

y

x = 1 0^{5^{y}}

Solve for

y, x = 1 0^{5^{y}}

\frac{ln ( \frac{l n ( x )}{l n ( 10 )} )}{ln ( 5 )}

What is the inverse of log_{10}(y)=5^x ?
The inverse of log_{10}(y)=5^x is (ln(\frac{ln(x))/(ln(10)))}{ln(5)}