Question

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

Answer 1

`\large\boxed{x=(5)/(2)=2(1)/(2)}`

Explanation:

`Domain:\ 4x>0\to x>0\\\\Use:\ \log_ab=c\iff a^c=b\ for\ a>0\ \wedge\ a\\eq1\ \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=(10)/(4)\\\\x=(10:2)/(4:2)\\\\x=(5)/(2)\\\\x=2(1)/(2)\in D`

Answer 2

x = 2.5

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