Verified answer

log(a) = b

a = 10^b

a^x = (10^b)^x

log a^x = log (10^bx)

log a^x = bx log (10), .. .note: log 10 = 1

log a^x = b(x) *(1)

hence, log a^x = bx ...

Remember that logarithms are basically exponents--literally.

log₁₀(a) = b if and only if a = 10^b

If a = 10^b, then aˣ = (10^b)ˣ = 10^(bx).

Therefore, log₁₀(aˣ) = log₁₀(10^(bx)) = bx

log(a^x)=xlog(a)=xb.

for example:

log(100^2)=2log(100)=2x2=4 (Since log(100)=2)

log(a) = b

--> 10^b=a

-->(10^b)^x=a^x

--> 10^(bx)=a^x

or log (a^x)=bx

Good luck !