Question

Convert 6^x = 1296 to a logarithmic equation

Answer 1

The base of the logarithm has not been specified, so it will be (logically) assumed that the base is 6.

6^x = 1296 = 6⁴
take logarithm to base 6 on each side:
x = 4

Answer 2

I know that x = 4 but the question asks to convert Convert 6^x = 1296 to a logarithmic equation. Here are my choices:

A. 6 = log_x 1296
B. 1296 = log_6 x
C. x = log_1296^6
D. x = log_6 1296

the line stands for the number or x being below the g in log, and the ^ stands for the number being above the 6 in Choice C.

Answer 3

If we consider the identity:

log_aa^b
=b
and apply the identity having a=6, b=x in the given question, you will be left with only two choices from which the right-hand-side will tell you which one to choose.
Make a choice and explain how you arrived at the choice you made.

Answer 4

I would say B because 1296 = log 6^4 Is this correct?

Answer 5

Not really, the relation is
log₆1296
=log₆ 6⁴
(= 4)

Since the left hand side says
6^x,
if you take log to the base 6, what would you get?

Answer 6

4? So the answer would be D?

D. x = log_6 1296

This was my second guess but I wasn't sure so log_6 1296 would work?

Answer 7

Yes, D would be fine.
If you proceed one step further to simplify the right hand side, you willfind that it equals 4, as you mentioned earlier.

Answer 8

Thanks for the explanation!