how to solve logarithms symbolically?

Question

log17(17)^(x+3)= log7(1)

thank you

Answer 1

(x+3) log17(17) = log7(1)

a^(loga b) = b
17^log17(17) = 17 so log17(17)=1
7^log7(1) = 1 so log7(1) = 0 (because7^0=1)
so we have
(x+3)(1)=0
x = -3