What is the answer to 8/3 =2^r ?

The answer to 8/3 =2^r is r=(ln(8/3))/(ln(2))

Solve for r: 8/3 =2^r

The solution is r=(ln(8/3))/(ln(2))

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\frac{8}{3} = 2^{r}

r = \frac{ln ( \frac{8}{3} )}{ln ( 2 )}

Decimal Notation

r = 1.41503 \dots

Solution steps

\frac{8}{3} = 2^{r}

Apply exponent rules

ln (\frac{8}{3}) = r ln (2)

Solve

ln (\frac{8}{3}) = r ln (2) : r = \frac{ln ( \frac{8}{3} )}{ln ( 2 )}

r = \frac{ln ( \frac{8}{3} )}{ln ( 2 )}

\frac{4 ^{x + 2}}{3 ^{x + 1}} = 16

2^{x} - 1 + 2^{x} + 1 = 2

7^{x - 1} + 7^{x} = 2744

\frac{1}{8} = \frac{4}{2 ^{\frac{t}{7}}}

5^{3 x - 1} = 25