Solve for x 2^(x-1)=10

Problem

2(x−1)=10

Solution

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

ln(2(x−1))=ln(10)

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

(x−1)*ln(2)=ln(10)

3. Isolate the term containing x by dividing both sides by ln(2)

x−1=ln(10)/ln(2)

4. Solve for x by adding 1 to both sides of the equation.

x=ln(10)/ln(2)+1

5. Simplify the expression using the change of base formula ln(a)/ln(b)=(log_b)(a) if desired.

x=(log_2)(10)+1

Final Answer

x=ln(10)/ln(2)+1

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