How do you solve 7-4logx=10?

Dec 19, 2015

${10}^{- \frac{3}{4}}$

Explanation:

$7 - 4 \log x = 10$

Subtract $7$ from both sides.

$- 4 \log x = 3$

Divide both sides by $- 4$.

$\log x = - \frac{3}{4}$

Recall that $\log x = {\log}_{10} x$.

Exponentiate both sides to undo the logarithm

${10}^{{\log}_{10} x} = {10}^{- \frac{3}{4}}$

$x = {10}^{- \frac{3}{4}}$

This can be written in a variety of different ways.

${10}^{- \frac{3}{4}} = \frac{1}{{10}^{\frac{3}{4}}} = \frac{1}{\sqrt[4]{{10}^{3}}} = \frac{1}{\sqrt[4]{1000}} \cong 0.1778$