Convert 6^x = 1296 to a logarithmic equation
The base of the logarithm has not been specified, so it will be (logically) assumed that the base is 6.
6x = 1296 = 64
take logarithm to base 6 on each side:
x = 4
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.
If we consider the identity:
logaab
=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.
I would say B because 1296 = log 6^4 Is this correct?
Not really, the relation is
log61296
=log6 64
(= 4)
Since the left hand side says
6x,
if you take log to the base 6, what would you get?
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?
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.
Thanks for the explanation!
To convert the equation 6^x = 1296 to a logarithmic equation, we need to express it in the form log(base b)(a) = x.
First, let's express 1296 as a power of 6. We can rewrite 1296 as 6^4 because 6^4 = 6 * 6 * 6 * 6 = 1296.
So, the equation becomes: 6^x = 6^4.
Now, we can rewrite it using logarithms: log(base 6)(6^x) = log(base 6)(6^4).
According to the logarithmic rule, log(base b)(b^x) = x, so we have: x = log(base 6)(6^4).
Therefore, the logarithmic equation form of 6^x = 1296 is x = log(base 6)(1296).