Question

Explain how to solve 5x − 2 = 8 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

Answer 1

Answer with explanation:

The given expression which we have to solve with the help of Logarithm is:

  5 x-2=8

Adding ,2 on both sides

⇒5 x-2+2=8+2

⇒5 x=10

Taking Log on both sides, having base 10

$\log_{10}5 x=\log_{10}10\\\\ \log_{10}5+\log_{10}x=1\\\\ \log_{a}a=1\\\\\log_{10}ab=\log_{10}a+\log_{10}b\\\\0.698+\log_{10}x=1\\\\ \log_{10}x=1 -0.698\\\\ \log_{10}x=0.302\\\\\frac{\log x}{\log 10}=0.302\\\\ \log x=\log 10^{0.302}\\\\x=10^{0.302}\\\\x=2.00447\\\\x=2.005$

Answer 2

Answer:

$x = 2$

Step-by-step explanation:

$5x - 2 = 8 \\ \\ 1. \: 5x = 10 \\ 2. \: \frac{5x}{5} = \frac{10}{5} \\ x = 2$