SOLUTION: 7^x-3/4=Square root of 6 PLEASE HELP! THANKS!

Question 112361: 7^x-3/4=Square root of 6
PLEASE HELP! THANKS!
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
Get rid of the on the left side by adding to both sides to get:
.

.
The right side of this equation is just a number. We can find that number using a calculator.
First, the fraction has a decimal equivalent of 0.75. (You can find that by using
a calculator to divide 4 (the denominator) into 3 (the numerator) and the calculator
will give you the answer of 0.75
.
Then you can use a calculator to find . The answer will be 2.449489743.
.
So the right side of the equation is 0.75 + 2.449489743 = 3.199489743
.
Therefore the equation is now:
.

.
You can solve this equation by taking the log to the base 10 of both sides to make the
equation become:
.

.
On the right side you can use a calculator to find log(3.199489743). This log is 0.505080722.
Substitute this value for the right side and the equation becomes:
.

.
When you take the log of a quantity raised to an exponent, you can bring the exponent out
as a multiplier of the log. This means that on the left side of the equation, the exponent
x can be brought out as the multiplier of the log to give:
.

.
Use a calculator to find . If you do you will find that it is 0.84509804.
Substitute this for the log and the equation becomes:
.

.
Solve for x by dividing both sides of this equation to get:
.

.
You can check this answer by using a calculator to raise 7 to the exponent 0.597659322
If you do, you will find that the answer is 3.199489741. Take 3/4 (or 0.75) from this
and you get that the left side of the original equation is 2.449489741. How does this left
side compare with which is the right side of the original equation?
As we found before, ... close enough. So the answer of x = 0.597659322
is correct.
.
Hope this helps you to understand the problem.
.

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