What is the answer to 7^{3x-2}+7^2=50 ?

The answer to 7^{3x-2}+7^2=50 is x= 2/3

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7^{3x-2}+7^2=50

7^{3 x - 2} + 7^{2} = 50

x = \frac{2}{3}

Decimal Notation

x = 0.66666 \dots

Solution steps

7^{3 x - 2} + 7^{2} = 50

Move

7^{2}

to the right side

7^{3 x - 2} = 50 - 7^{2}

Simplify

7^{3 x - 2} = 1

Apply exponent rules

(3 x - 2) ln (7) = ln (1)

Solve

(3 x - 2) ln (7) = ln (1) : x = \frac{2}{3}

x = \frac{2}{3}

5^{2 x - 4} = 2^{5 x}

5 e^{x + 2} = 7

2^{x - 1} + 2^{x - 2} + 2^{x - 3} = 112

e^{e^{x}} = 1

e^{e^{x}} = 5