382/HK16. problem / Math - Solved Math Problems

MR-382 / 6. problem

Solve the following equation on the set of real numbers!
Round your answer to three decimal places!

$2^{x} = 10$

Source: Magyarország: Unified final exam for high schools - Mathematics - intermediate level - 03.05.2016. - 6..)

Algebra → Exponential equations and inequalities → Exponential equations

2^{x} = 10

2^{x} = 10 l o g_{10} ()

\log_{10} (2^{x}) = \log_{10} 10

x \cdot \log_{10} 2 = 1

x = \frac{1}{\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