Solve 6786=4367^r*6

$$6786 = { 4367 }^{ r \times 6 }$$

Solve for r

$$r=\frac{\log_{4367}\left(6786\right)}{6}\approx 0.175431366$$

Steps Using Definition of Logarithm

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

$$4367^{r\times 6}=6786$$

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

$$4367^{6r}=6786$$

Take the logarithm of both sides of the equation.

$$\log(4367^{6r})=\log(6786)$$

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

$$6r\log(4367)=\log(6786)$$

Divide both sides by \log(4367).

$$6r=\frac{\log(6786)}{\log(4367)}$$

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

$$6r=\log_{4367}\left(6786\right)$$

Divide both sides by 6.

$$r=\frac{\log_{4367}\left(6786\right)}{6}$$