SOLUTION: (2/3)log

SOLUTION: (2/3)log_x512=2

Question 114268This question is from textbook
: (2/3)log_x512=2 This question is from textbook

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
If I interpret your problem correctly it is:
.

.
Since the is a multiplier of the log function, by the rules of logarithms it
can be taken inside as an exponent of the quantity on which the log is operating.
In other words an equivalent equation is:
.

.
Now let's calculate . This is equivalent to which is
equivalent to the cube root of 512 squared. Calculator time ... when you square 512 you
get 262144. And when you take the cube root of 262144 you get 64. So in the equation you
can replace by and the equation becomes:
.

.
Now convert this from logarithmic form to exponential form. The rule is:
.
is equivalent to the exponential form .
.
By comparing this rule to the equation we have, we can say that:
.
is equivalent to the exponential form
.
Take the square root of both sides of the equivalent exponential form and you get:
.

.
so the base of the logarithm that makes the given problem true is 8 and you can write
the original problem statement as:
.

.
Hope this helps you to understand the problem.
.

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