Solve for x 4^(3x+1)=64

Problem

4(3*x+1)=64

Solution

1. Identify the base on the left side of the equation, which is 4

2. Rewrite the right side of the equation, 64 as a power of 4 to create a common base.

64=4

3. Substitute the new expression for 64 back into the original equation.

4(3*x+1)=4

4. Apply the property of equality for exponential functions, which states that if by=bz then y=z

3*x+1=3

5. Isolate the term containing x by subtracting 1 from both sides.

3*x=2

6. Solve for x by dividing both sides by 3

x=2/3

Final Answer

4(3*x+1)=64⇒x=2/3

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