What is the integral from 0 to log_{3 of (8)}3^x ?

The integral from 0 to log_{3 of (8)}3^x is 7/(ln(3))

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integral from 0 to log_{3 of (8)}3^x

\int_{0}^{l o g_{3} (8)} 3^{x} d x

\frac{7}{ln ( 3 )}

Decimal

6.37167 \dots

Solution steps

\int_{0}^{l o g_{3} (8)} 3^{x} d x

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

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

Simplify

lo g_{3} (8) : 3 lo g_{3} (2)

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

Compute the boundaries:

\frac{7}{ln ( 3 )}

= \frac{7}{ln ( 3 )}

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What is the integral from 0 to log_{3 of (8)}3^x ?
The integral from 0 to log_{3 of (8)}3^x is 7/(ln(3))