Question 248608
Unless an exponent is just a single number or variable, please put parentheses around it. I can't tell if the left side is:
{{{7^(x^2)-15}}}, {{{(7^x)^2-15}}} or {{{7^(x^2-15)}}}
These are all different and will have different solutions. So I really can't help you much until I know which is correct.<br>
But I can say that the solution will probably take advantage of the fact that 49 is a power of 7:
{{{49^x = (7^2)^x = 7^(2x)}}}
(The last part comes from the rule for exponents: {{{(a^p)^q = a^(p*q)}}})<br>
If the left side is {{{7^(x^2-15)}}}, then the problem is easier than the other two possibilities:
{{{7^(x^2-15) = 7^(2x)}}}
With both the left side and the right side being a powers of 7, the exponents must be equal:
{{{x^2-15 = 2x}}}
This is now a quadratic equation. So we'll get one side equal to zero (by subtracting 2x):
{{{x^2-2x-15 = 0}}}
Factor:
{{{(x-5)(x+3) = 0}}}
Use the Zero Product Property:
{{{x-5 = 0}}} or {{{x+3 = 0}}}
Solve:
{{{x = 5}}} or {{{x = -3}}}