MR-382 / 6. problem

Solve the following equation on the set of real numbers!

Round your answer to three decimal places!

${2}^{x}=10$

$${2}^{x}=10$$

$${2}^{x}=10{}\overline{)lo{g}_{10}\left(\right)}$$

$$$$$${\mathrm{log}}_{10}\left({2}^{x}\right)={\mathrm{log}}_{10}10$$

$$$$$$x\xb7{\mathrm{log}}_{10}2=1$$

$$$$$$x=\frac{1}{{\mathrm{log}}_{10}2}$$

$$$$$$x=\frac{1}{0.301}$$

$$$$$$x=3,322$$

Take the logarithm with base 10 from the left and right sides!

$$x=3,322$$