Solve log_{6}2*log_{6}6^2=log_{6}2^2

$$\log _ { 6 } 2 \times \log _ { 6 } 6 ^ { 2 } = \log _ { 6 } 2 ^ { 2 }$$

Verify

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\log_{6}\left(2\log_{6}\left(36\right)\right)=\log_{6}\left(2^{2}\right)$$

The base 6 logarithm of 36 is 2.

$$\log_{6}\left(2\times 2\right)=\log_{6}\left(2^{2}\right)$$

Multiply 2 and 2 to get 4.

$$\log_{6}\left(4\right)=\log_{6}\left(2^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$\log_{6}\left(4\right)=\log_{6}\left(4\right)$$

Subtract \log_{6}\left(4\right) from both sides.

$$\log_{6}\left(4\right)-\log_{6}\left(4\right)=0$$

Combine \log_{6}\left(4\right) and -\log_{6}\left(4\right) to get 0.

$$0=0$$

Compare 0 and 0.

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