Question

log4(x-3)=2
4^2=x-3
16=x-3
19=x

Does this mean the solution would be x=19 or no solution? How would I check this to know if 19 is a solution. I know I plug it back in. Like so:
log4(19-3)=2
4^2=19-3
16=16
Did i check correctly?

Answer 1

your solution is correct

to check, you must go back to the original equation

LS = log4 (19-3)
= log 4 (16)
= 2 -----> what must be exponent on 4 to get 16 ?
= RS

so x = 19