Question

Explain how to solve 5x − 2 = 8 using the change of base formula log_b of y = log y / log b.

Answer 1

Answer with explanation:

The equation is

  5 x-2 =8

Adding 2 on both sides

→5 x-2+2=8+2

→5 x=10

Dividing both sides by,5, we get

→x=2

Using the concept of Logarithms

$1.\log_{a}b=\frac{\log b}{\log a}\\\\2.\log ab=\log a +\log b\\\\\rightarrow \log_{10}{5 x}=\log_{10} 10\\\\\rightarrow \log_{10}5+\log_{10} x=1\\\\0.698+\log_{10} x=1\\\\\log_{10} x=1-0.698\\\\ \frac{\log x}{\log 10}=0.302\\\\ \log x=(\log 10^{0.302})\\\\ \log x=\log 2.044\\\\x=2.004472$

Gives, x=2.005 (Approx)