What is the integral from 0 to log_{8 of (5)}8^x ?

The integral from 0 to log_{8 of (5)}8^x is 4/(3ln(2))

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integral from 0 to log_{8 of (5)}8^x

\int_{0}^{l o g_{8} (5)} 8^{x} d x

\frac{4}{3 ln ( 2 )}

Decimal

1.92359 \dots

Solution steps

\int_{0}^{l o g_{8} (5)} 8^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= [\frac{8 ^{x}}{ln ( 8 )}]_{0}^{l o g_{8} (5)}

Simplify

ln (8) : 3 ln (2)

= [\frac{8 ^{x}}{3 ln ( 2 )}]_{0}^{l o g_{8} (5)}

Compute the boundaries:

\frac{4}{3 ln ( 2 )}

= \frac{4}{3 ln ( 2 )}

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What is the integral from 0 to log_{8 of (5)}8^x ?
The integral from 0 to log_{8 of (5)}8^x is 4/(3ln(2))