What is the answer to 49^x=343^{2x-3} ?

The answer to 49^x=343^{2x-3} is x= 9/4

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49^x=343^{2x-3}

4 9^{x} = 34 3^{2 x - 3}

x = \frac{9}{4}

Decimal Notation

x = 2.25

Solution steps

4 9^{x} = 34 3^{2 x - 3}

Apply exponent rules

2 x = 3 (2 x - 3)

Solve

2 x = 3 (2 x - 3) : x = \frac{9}{4}

x = \frac{9}{4}

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

(\frac{1}{2})^{2 x} = 2^{3 - x}

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

3^{2 x} - 4 \times 3^{x} + 3 = 0

10 \cdot 3^{x + 3} = 60