Solve 5*18^6x=26

$$5 \cdot 18 ^ { 6 x } = 26$$

Solve for x

$$x=\frac{\log_{18}\left(\frac{26}{5}\right)}{6}\approx 0.095066123$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$5\times 18^{6x}=26$$

Divide both sides by 5.

$$18^{6x}=\frac{26}{5}$$

Take the logarithm of both sides of the equation.

$$\log(18^{6x})=\log(\frac{26}{5})$$

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

$$6x\log(18)=\log(\frac{26}{5})$$

Divide both sides by \log(18).

$$6x=\frac{\log(\frac{26}{5})}{\log(18)}$$

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

$$6x=\log_{18}\left(\frac{26}{5}\right)$$

Divide both sides by 6.

$$x=\frac{\ln(\frac{26}{5})}{6\ln(18)}$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{3\ln(18)}+\frac{\log_{18}\left(\frac{26}{5}\right)}{6}$$

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