What is the answer to (2/3)^{5x+2}=(3/2)^{2x} ?

The answer to (2/3)^{5x+2}=(3/2)^{2x} is x=-2/7

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(2/3)^{5x+2}=(3/2)^{2x}

(\frac{2}{3})^{5 x + 2} = (\frac{3}{2})^{2 x}

x = - \frac{2}{7}

Decimal Notation

x = - 0.28571 \dots

Solution steps

(\frac{2}{3})^{5 x + 2} = (\frac{3}{2})^{2 x}

Apply exponent rules

- (5 x + 2) = 2 x

Solve

- (5 x + 2) = 2 x : x = - \frac{2}{7}

x = - \frac{2}{7}

144 \cdot 2^{\frac{x}{3}} = 1616

3^{4 x + 1} - 5 = 22

\frac{2 ^{x^{2}}}{4 ^{x}} = 16

e^{- x} - x + 1 = 0

9^{x + 1} - 28 \cdot 3^{x} + 3 = 0

What is the answer to (2/3)^{5x+2}=(3/2)^{2x} ?
The answer to (2/3)^{5x+2}=(3/2)^{2x} is x=-2/7
Solve for x: (2/3)^{5x+2}=(3/2)^{2x}
The solution is x=-2/7