SOLUTION: please solve for x : {{{100^(x^2)=10^(5x-3)}}}

Question 131921: please
solve for x :
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given to solve for x:
.

.
Take the base 10 logarithm of both sides:
.

.
Apply the rule of logarithms that says an exponent comes out as the multiplier of the logarithm.
When you apply that rule, the problem becomes:
.

.
But your calculator will tell you that and
Make these two substitutions into the equation and it becomes:
.

.
which simplifies to:
.

.
subtract 5x - 3 from both sides to get the equation into the standard form of:
.

.
The left side of this equation factors to give:
.

.
Notice that this equation will be true if either of the two factors is equal to zero ... because
a multiplication by zero on the left side makes the entire left side equal to zero and
therefore equal to the right side.
.
So either or
.
Solve these two equations. From you can see that and from
you get
.
Therefore, the two answers to this problem are x = 1 and x = 1.5
.
Hope this helps you to understand the problem and how it can be worked to get the answer.
.
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