Solve 2*7^2n-98=0

$$2 \times 7 ^ { 2 n } - 98 = 0$$

Solve for n

$$n=1$$

Steps Using Definition of Logarithm

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

$$2\times 7^{2n}-98=0$$

Add 98 to both sides of the equation.

$$2\times 7^{2n}=98$$

Divide both sides by 2.

$$7^{2n}=49$$

Take the logarithm of both sides of the equation.

$$\log(7^{2n})=\log(49)$$

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

$$2n\log(7)=\log(49)$$

Divide both sides by \log(7).

$$2n=\frac{\log(49)}{\log(7)}$$

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

$$2n=\log_{7}\left(49\right)$$

Divide both sides by 2.

$$n=\frac{2}{2}$$

Solve for n (complex solution)

$$n=\frac{\pi n_{1}i}{\ln(7)}+1$$

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