What is the answer to (4e^{3x}-5)/(e^{3x)-1}=3 ?

The answer to (4e^{3x}-5)/(e^{3x)-1}=3 is x=(ln(2))/3

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(4e^{3x}-5)/(e^{3x)-1}=3

\frac{4 e ^{3 x} - 5}{e ^{3 x} - 1} = 3

x = \frac{ln ( 2 )}{3}

Solution steps

\frac{4 e ^{3 x} - 5}{e ^{3 x} - 1} = 3

Multiply both sides by

e^{3 x} - 1

\frac{4 e ^{3 x} - 5}{e ^{3 x} - 1} (e^{3 x} - 1) = 3 (e^{3 x} - 1)

Simplify

4 e^{3 x} - 5 = 3 (e^{3 x} - 1)

Expand

3 (e^{3 x} - 1) : 3 e^{3 x} - 3

4 e^{3 x} - 5 = 3 e^{3 x} - 3

Move

5

to the right side

4 e^{3 x} = 3 e^{3 x} + 2

Move

3 e^{3 x}

to the left side

e^{3 x} = 2

Apply exponent rules

3 x = ln (2)

Solve

3 x = ln (2) : x = \frac{ln ( 2 )}{3}

x = \frac{ln ( 2 )}{3}

Verify Solutions:

x = \frac{ln ( 2 )}{3}

True

The solution is

x = \frac{ln ( 2 )}{3}

350000 = 400 \cdot (1 - e^{- 0.15 t})

3^{x} + 1 = 3^{5}

3^{x^{2} + x} = 9

e^{(l n (0.1)) t} = 0.9

5^{x^{2} - 3 x} = 625

What is the answer to (4e^{3x}-5)/(e^{3x)-1}=3 ?
The answer to (4e^{3x}-5)/(e^{3x)-1}=3 is x=(ln(2))/3