how do i solve this logarithm?

Question

log(base4)(x-1) - 2 = log(base4)3

how do i get the value of x?

Answer 1

write the 2 as 2*log(base4)(4) = log(base4)(16)

So applying law of logs
(x-1) / 16 = 3
x = 49

Answer 2

I'll show you the way I remember these types of problems.

log (base10) 100 = 2
therefore 10² = 100

In your problem rearranging terms we go from
log(base4)(x-1) - 2 = log(base4)3

to
log(base4)(x-1) - log(base4)3 = 2
log(base4)((x-1)/3) = 2

Now using my memory aid from above

4² = (x - 1)/3

x - 1 = 48

x = 49

Hope this helps you.
.

Answer 3

log(base4)(x-1) - 2 = log(base4)3
log(base4)(x-1-log(base4 )16)=log(base4)3
log(base4)(x-1)/16 =log(base4)3
x-1/16=3
x-1=48
x=49.