Question

can you prove this statement using properties of logarithms?
\log_{7}7^{8} = \left(\log_{7}7\
ight)^{8}
yes
no

Explanation:

Step1: Simplify left-hand side

Use power rule: $\log_b a^n = n\log_b a$
$\log_7 7^8 = 8\log_7 7$
Since $\log_7 7 = 1$, this becomes $8 \times 1 = 8$

Step2: Simplify right-hand side

First calculate inner term: $\log_7 7 = 1$
Then raise to the 8th power: $1^8 = 1$

Step3: Compare both sides

Left-hand side = 8, Right-hand side = 1
$8
eq 1$, so the statement is false.

Answer:

no