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

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

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(e^x-2)/3 =e^{2x}-4

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

x = ln (2)

Decimal Notation

x = 0.69314 \dots

Solution steps

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

Multiply both sides by

3

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

Simplify

e^{x} - 2 = 3 e^{2 x} - 12

Apply exponent rules

e^{x} - 2 = 3 (e^{x})^{2} - 12

Rewrite the equation with

e^{x} = u

u - 2 = 3 (u)^{2} - 12

Solve

u - 2 = 3 u^{2} - 12 : u = 2, u = - \frac{5}{3}

u = 2, u = - \frac{5}{3}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 2 : x = ln (2)

Solve

e^{x} = - \frac{5}{3} :

No Solution for

x \in R

x = ln (2)

1 6^{x} = \frac{1}{64}

240 = 200 e^{x \cdot \frac{6}{12}}

(4^{x}) (4^{5}) = 4^{8}

2 5^{- x} = 5^{x + 7}

2^{x} + 4 = 2^{3} x - 1

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