Solve for x 4^x=22

Problem

4=22

Solution

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

ln(4)=ln(22)

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

x*ln(4)=ln(22)

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

x=ln(22)/ln(4)

4. Simplify the expression if needed. Since 4=2 we can write ln(4) as 2*ln(2)

x=ln(22)/(2*ln(2))

Final Answer

x=ln(22)/ln(4)

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