What is the answer to ln((4x+1)/3)=2 ?

The answer to ln((4x+1)/3)=2 is x=(3e^2-1)/4

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ln((4x+1)/3)=2

ln (\frac{4 x + 1}{3}) = 2

x = \frac{3 e ^{2} - 1}{4}

Decimal Notation

x = 5.29179 \dots

Solution steps

ln (\frac{4 x + 1}{3}) = 2

Apply log rules

\frac{4 x + 1}{3} = e^{2}

Multiply both sides by

3

\frac{4 x + 1}{3} \cdot 3 = e^{2} \cdot 3

Simplify

4 x + 1 = e^{2} \cdot 3

Solve

4 x + 1 = e^{2} \cdot 3 : x = \frac{3 e ^{2} - 1}{4}

x = \frac{3 e ^{2} - 1}{4}

Verify Solutions:

x = \frac{3 e ^{2} - 1}{4}

True

The solution is

x = \frac{3 e ^{2} - 1}{4}

lo g_{5} (13 x) = - 2

0.2 = lo g_{10} (x)

0 = lo g_{\frac{1}{4}} (- x + 4)

lo g_{3} (x + 1) - lo g_{3} (x - 2) = 2

- 1 = ln (8 x)

What is the answer to ln((4x+1)/3)=2 ?
The answer to ln((4x+1)/3)=2 is x=(3e^2-1)/4
Solve for x: ln((4x+1)/3)=2
The solution is x=(3e^2-1)/4