Solve 3(1/log_{5625}+2/5div8/25)^2=

$$3 ( \frac { 1 } { \log _ { 5 } 625 } + \frac { 2 } { 5 } \div \frac { 8 } { 25 } ) ^ { 2 } =$$

Evaluate

$$\frac{27}{4}=6.75$$

Solution Steps

The base 5 logarithm of 625 is 4.

$$3\left(\frac{1}{4}+\frac{\frac{2}{5}}{\frac{8}{25}}\right)^{2}$$

Divide \frac{2}{5} by \frac{8}{25} by multiplying \frac{2}{5} by the reciprocal of \frac{8}{25}.

$$3\left(\frac{1}{4}+\frac{2}{5}\times \frac{25}{8}\right)^{2}$$

Multiply \frac{2}{5} and \frac{25}{8} to get \frac{5}{4}.

$$3\left(\frac{1}{4}+\frac{5}{4}\right)^{2}$$

Add \frac{1}{4} and \frac{5}{4} to get \frac{3}{2}.

$$3\times \left(\frac{3}{2}\right)^{2}$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$3\times \frac{9}{4}$$

Multiply 3 and \frac{9}{4} to get \frac{27}{4}.

$$\frac{27}{4}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {2}} = 6\frac{3}{4} = 6.75$$