e Try to find x on the left-hand side of the original expressions. What do the logarithm and the exponent do to each other?
A
a x=2
B
b x=3
C
c x=4
D
d x=4
E
e A logarithm function and an exponential function undo each other if they have the same base.
a Notice that this is a logarithm with a base of 8. This means if we can rewrite the logarithm's argument as a power of 8, we can determine the result by looking at the exponent.
log_8 8^b = b
Since 64 can be rewritten as a power of 8, we can use this identity.
e In Part C and Part D of this exercise we have the following.
Part C: log_3 3^4 = 4 [0.5em]
Part D: 10^(log_(10) 4)= 4
This tells us that a logarithm function and an exponential function undo each other if they have the same base. We can write this generally as follows.
log_b b^c = c ⇔ b^(log_b c)= c
