Solve 2^60=8*2^x

$${ 2 }^{ 60 } =8 \times { 2 }^{ x }$$

Solve for x

$$x=57$$

Steps Using Definition of Logarithm

Calculate 2 to the power of 60 and get 1152921504606846976.

$$1152921504606846976=8\times 2^{x}$$

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

$$8\times 2^{x}=1152921504606846976$$

Divide both sides by 8.

$$2^{x}=\frac{1152921504606846976}{8}$$

Divide 1152921504606846976 by 8 to get 144115188075855872.

$$2^{x}=144115188075855872$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(144115188075855872)$$

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

$$x\log(2)=\log(144115188075855872)$$

Divide both sides by \log(2).

$$x=\frac{\log(144115188075855872)}{\log(2)}$$

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

$$x=\log_{2}\left(144115188075855872\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+57$$

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