What is the answer to 3(4^x)+4^{x-1}=52 ?

The answer to 3(4^x)+4^{x-1}=52 is x=2

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3(4^x)+4^{x-1}=52

3 (4^{x}) + 4^{x - 1} = 52

x = 2

Solution steps

3 (4^{x}) + 4^{x - 1} = 52

Factor

3 \cdot 4^{x} + 4^{x - 1} : 13 \cdot 4^{x - 1}

13 \cdot 4^{x - 1} = 52

Divide both sides by

13

4^{x - 1} = 4

Apply exponent rules

x - 1 = 1

Solve

x - 1 = 1 : x = 2

x = 2

4^{2 x} + 12 = 2^{2 x + 3}

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

2 5^{x - 1} + 100 = 5^{2 x - 1}

2^{2 x + 1} = 2^{x + 2}

6^{x + 2} = 1 3^{9 x}

What is the answer to 3(4^x)+4^{x-1}=52 ?
The answer to 3(4^x)+4^{x-1}=52 is x=2
Solve for x: 3(4^x)+4^{x-1}=52
The solution is x=2