Solve log10^5*10^-3/10^7=

$$\log \frac { 10 ^ { 5 } \times 10 ^ { - 3 } } { 10 ^ { 7 } } =$$

Evaluate

$$-5$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and -3 to get 2.

$$\log_{10}\left(\frac{10^{2}}{10^{7}}\right)$$

Rewrite 10^{7} as 10^{2}\times 10^{5}. Cancel out 10^{2} in both numerator and denominator.

$$\log_{10}\left(\frac{1}{10^{5}}\right)$$

Calculate 10 to the power of 5 and get 100000.

$$\log_{10}\left(\frac{1}{100000}\right)$$

The base 10 logarithm of \frac{1}{100000} is -5.

$$-5$$

Factor

$$-5$$