Solve for x 2^x=7

Problem

2=7

Solution

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

ln(2)=ln(7)

2. Use the power rule for logarithms, which states that ln(ab)=b*ln(a) to bring the variable x down from the exponent.

x*ln(2)=ln(7)

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

x=ln(7)/ln(2)

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

x=(log_2)(7)

Final Answer

x=ln(7)/ln(2)

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