Question

Solve log (4x+5)=2. Round to the nearest thousandth if necessary.

Answer 1

10%5E2+=+4x+%2B+5
100+=+4x+%2B+5
4x+=+95
x+=+23.75
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Answer 2

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 $x$

$4x+5-5=100-5\\4x=95\\\frac{4x}{4}=\frac{95}{4}\\x=\frac{95}{4}$