To solve the equation [tex]\(7^{2x} = 49\)[/tex]:
1. Express 49 as a power of 7: Notice that 49 can be written as [tex]\(7^2\)[/tex].
[tex]\[
49 = 7^2
\][/tex]
2. Substitute [tex]\(7^2\)[/tex] into the equation: Replace 49 in the given equation with [tex]\(7^2\)[/tex].
[tex]\[
7^{2x} = 7^2
\][/tex]
3. Set the exponents equal to each other: Since the bases (7) are the same, we can equate the exponents.
[tex]\[
2x = 2
\][/tex]
4. Solve for [tex]\(x\)[/tex]: Divide both sides of the equation by 2.
[tex]\[
x = \frac{2}{2} = 1
\][/tex]
So, the solution to the equation [tex]\(7^{2x} = 49\)[/tex] is [tex]\(x = 1\)[/tex].
