Solve for x 2^(3x)=34

Problem

2(3*x)=34

Solution

1. Apply the logarithm to both sides of the equation to isolate the exponent. We will use the natural logarithm ln()

ln(2(3*x))=ln(34)

2. Use the power rule for logarithms, which states that ln(ab)=b*ln(a) to move the variable out of the exponent.

3*x*ln(2)=ln(34)

3. Isolate the variable x by dividing both sides of the equation by 3*ln(2)

x=ln(34)/(3*ln(2))

4. Simplify the expression if a decimal approximation is required, or keep it in exact logarithmic form.

x=ln(34)/ln(2)

x=ln(34)/ln(8)

Final Answer

x=ln(34)/(3*ln(2))

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