Solve for x 5^x=8

Problem

5=8

Solution

1. Apply the logarithm to both sides of the equation to isolate the variable x You can use the natural logarithm ln() or the common logarithm (log_)()

ln(5)=ln(8)

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

x*ln(5)=ln(8)

3. Isolate x by dividing both sides of the equation by ln(5)

x=ln(8)/ln(5)

4. Apply the change of base formula if a single logarithm is preferred, noting that ln(8)/ln(5)=(log_5)(8)

x=(log_5)(8)

Final Answer

x=ln(8)/ln(5)

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