Asked by Audrey

Convert 6^x = 1296 to a logarithmic equation

Answers

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

6<sup>x</sup> = 1296 = 6<sup>4</sup>
take logarithm to base 6 on each side:
x = 4
Answered by Audrey
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.
Answered by MathMate
If we consider the identity:

log<sub>a</sub>a<sup>b</sup>
=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.
Answered by Audrey
I would say B because 1296 = log 6^4 Is this correct?
Answered by MathMate
Not really, the relation is
log<sub>6</sub>1296
=log<sub>6</sub> 6<sup>4</sup>
(= 4)

Since the left hand side says
6<sup>x</sup>,
if you take log to the base 6, what would you get?
Answered by Audrey
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?
Answered by MathMate
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.
Answered by Audrey
Thanks for the explanation!
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