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