Solve 7^5*7=7^x

$${ 7 }^{ 5 } \times 7= { 7 }^{ x }$$

Solve for x

$$x=6$$

Steps Using Definition of Logarithm

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$7^{6}=7^{x}$$

Calculate 7 to the power of 6 and get 117649.

$$117649=7^{x}$$

Swap sides so that all variable terms are on the left hand side.

$$7^{x}=117649$$

Take the logarithm of both sides of the equation.

$$\log(7^{x})=\log(117649)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$x\log(7)=\log(117649)$$

Divide both sides by \log(7).

$$x=\frac{\log(117649)}{\log(7)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$x=\log_{7}\left(117649\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(7)}+6$$

$$n_{1}\in \mathrm{Z}$$