Solve for x 2^x=5

Problem

2=5

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(2)=ln(5)

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(2)=ln(5)

3. Divide both sides by ln(2) to solve for x

x=ln(5)/ln(2)

4. Apply the change of base formula if a single logarithm is preferred, noting that (log_c)(a)/(log_c)(b)=(log_b)(a)

x=(log_2)(5)

Final Answer

x=ln(5)/ln(2)

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