Question

log8(x+1)=2/3 (a small 8)

Answer 1

\[\log_ab = c \iff a^c =b \]

Answer 2

\[x+1=8^{\frac{2}{3}}\]
\[x+1=\sqrt[3]8^2\]
\[x+1=2^2\]
\[x+1=4\]
\[x=3\]

Answer 3

\[\log_8(x+1)=\frac{2}{3}\] now we make both of the sides an exponent of 8. It'll look like this
\[8^{\log_8(x+1)}=8^{\frac{2}{3}}\] the left side simply becomes x+1 because of a common cancellation rule of logs. In general,
\[a^{\log_ab}=b\] since log base a of b is the exponent we must raise a to in order to get b, if we make log base a of b an exponent of a, we get b
the left side is
\[8^\frac{2}{3}=\sqrt[3]{8}^2=2^2=4\]
therefore, x+1=4, and x=3