Solve for x 8^(3x)=360

Problem

8(3*x)=360

Solution

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

ln(8(3*x))=ln(360)

2. Use the power rule of logarithms, which states that ln(ab)=b*ln(a) to move the exponent in front of the logarithm.

3*x*ln(8)=ln(360)

3. Isolate the variable x by dividing both sides of the equation by 3*ln(8)

x=ln(360)/(3*ln(8))

4. Simplify the expression using the property 3*ln(8)=ln(8) Since 8=512 the denominator can be written as ln(512)

x=ln(360)/ln(512)

5. Calculate the numerical value using a calculator for an approximate decimal answer.

x≈0.9435

Final Answer

x=ln(360)/(3*ln(8))≈0.9435

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