Question

Solve 9x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b.

Answer 1

`x = (7)/(9)`

Explanation:

`9x + 4 = 11 \\ \\ 1. \: 9x = 11 - 4 \\ 2. \: 9x = 7 \\ x = (7)/(9)`

Answer 2

Answer with explanation:

The given equation in one variable is:

→ 9 x +4 =11

Subtracting 4 from both sides

→9 x +4 -4=11 -4

→ 9 x=7

Taking log on both sides

→log ( 9 x)= log 7-----log having base 10 is considered.

→ log 9 + log x= log 7

→ 0.95424 + log x= 0.8450

→ log x=0.8450 - 0.9542

→ log x= -0.1092

`\rightarrow(\log x)/(\log 10)=-0.1092\\\\\rightarrow \log x=-0.1092 * \log 10\\\\\rightarrow \log x=\log 10^(-0.1092)\\\\\rightarrow x=10^(-0.1092)\\\\\rightarrow x=0.77767\\\\x=0.778`