Solve for x 4^x=19

Problem

4=19

Solution

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

ln(4)=ln(19)

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

x*ln(4)=ln(19)

3. Isolate x by dividing both sides of the equation by ln(4)

x=ln(19)/ln(4)

4. Apply the change of base formula if a single logarithm is preferred, noting that ln(19)/ln(4)=(log_4)(19)

x=(log_4)(19)

Final Answer

x=ln(19)/ln(4)

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