Solve log_{10}[10^2(10^4)^3/10^6]

$$\log _ { 10 } [ \frac { 10 ^ { 2 } ( 10 ^ { 4 } ) ^ { 3 } } { 10 ^ { 6 } } ]$$

Evaluate

$$8$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\log_{10}\left(\frac{10^{2}\times 10^{12}}{10^{6}}\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 12 to get 14.

$$\log_{10}\left(\frac{10^{14}}{10^{6}}\right)$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 14 to get 8.

$$\log_{10}\left(10^{8}\right)$$

Calculate 10 to the power of 8 and get 100000000.

$$\log_{10}\left(100000000\right)$$

The base 10 logarithm of 100000000 is 8.

$$8$$

Factor

$$2^{3}$$