Answer:
The solution is \(x=\frac{95}{4}=23.75\).
Step-by-step explanation:
To solve the equation \(\log _{10}\left(4x+5\right)=2\).
Use the logarithmic definition: \(\mathrm{If}\:\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c\)
\(\log _{10}\left(4x+5\right)=2\quad \Rightarrow \quad \:4x+5=10^2\)
Simplify
\(4x+5=100\)
Next, solve for \(x\)
\(4x+5-5=100-5\\4x=95\\\frac{4x}{4}=\frac{95}{4}\\x=\frac{95}{4}\)
