Question

Solve each equation. 2+3log(4x)=5

Answer 1

Answer:

$\large\boxed{x=\dfrac{5}{2}=2\dfrac{1}{2}}$

Step-by-step explanation:

$Domain:\ 4x>0\to x>0\\\\Use:\ \log_ab=c\iff a^c=b\ for\ a>0\ \wedge\ a\neq1\ \wedge\ b>0\\\\\log(x)=\log_{10}(x)\\=============================\\\\2+3\log(4x)=5\qquad\text{subtract 2 from both sides}\\\\3\log(4x)=3\qquad\text{divide both sides by 3}\\\\\log(4x)=1\iff4x=10^1\\\\4x=10\qquad\text{divide both sides by 4}\\\\x=\dfrac{10}{4}\\\\x=\dfrac{10:2}{4:2}\\\\x=\dfrac{5}{2}\\\\x=2\dfrac{1}{2}\in D$

Answer 2

Answer:

x = 2.5

Step-by-step explanation:

2+3log(4x)=5

Subtract 2 from each side

2-2+3log(4x)=5-2

3log (4x) = 3

Divide by 3

3/3 log (4x) = 3/3

log (4x) =1

Raise each side to the power of 10 (The implied base on the log is 10)

10^ log (4x) = 10 ^1

4x = 10

Divide each side by 4

4x/4 =10/4

x = 2.5