Solve log1125=log(3^2*5^3)

$$\log 1125 = \log ( 3 ^ { 2 } \cdot 5 ^ { 3 } )$$

Verify

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\log_{10}\left(1125\right)=\log_{10}\left(9\times 5^{3}\right)$$

Calculate 5 to the power of 3 and get 125.

$$\log_{10}\left(1125\right)=\log_{10}\left(9\times 125\right)$$

Multiply 9 and 125 to get 1125.

$$\log_{10}\left(1125\right)=\log_{10}\left(1125\right)$$

Subtract \log_{10}\left(1125\right) from both sides.

$$\log_{10}\left(1125\right)-\log_{10}\left(1125\right)=0$$

Combine \log_{10}\left(1125\right) and -\log_{10}\left(1125\right) to get 0.

$$0=0$$

Compare 0 and 0.

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