Question

Solve for x.

Answer 1

\[(\sqrt{7})^6x = 49^x -6\]

Answer 2

\(\large \bf (\sqrt{7})^6x = 49^{x -6} ?\)

Answer 3

@jdoe0001 No, 6x is ^

Answer 4

\(\large \bf (\sqrt{7})^{6x} = 49^{x -6}\)?

Answer 5

well. hmmm
let us recall that hmm one sec

Answer 6

\(\large \bf {
(\sqrt{7})^{6x} = 49^{x -6}
\\ \quad \\
a^{\frac{{\color{blue} n}}{{\color{red} m}}} \implies \sqrt[{\color{red} m}]{a^{\color{blue} n}} \qquad \qquad

\sqrt[{\color{red} m}]{a^{\color{blue} n}}\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}}\qquad thus
\\ \quad \\
(\sqrt[{\color{red}{ 2 }}]{7^{\color{blue}{ 1}}})^{6x} = 49^{x -6}\implies (7^{\frac{{\color{blue}{ 1}}}{{\color{red}{ 2}}}})^{6x}=49^{x -6}\qquad {\color{brown}{ 49=7^2}}\qquad thus
\\ \quad \\
(7^{\frac{1}{2}})^{6x}=(7^2)^{x-6}
}\)

so.. should be fairly simple from there I'd think

Answer 7

Woah!!! this invisible guy is a good helper. :)

Answer 8

@jim_thompson5910 How do I finish this?

Answer 9

Using what jdoe0001 wrote, you can then set the exponents equal to each other and solve

\[\Large \frac{1}{2}*(6x) = 2*(x-6)\]