Solve for x 3^x=2

Problem

3=2

Solution

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

ln(3)=ln(2)

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(3)=ln(2)

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

x=ln(2)/ln(3)

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

x=(log_3)(2)

Final Answer

x=ln(2)/ln(3)

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