Solve for x 2700=300*2^(10x)

Problem

2700=300⋅2(10*x)

Solution

1. Divide both sides of the equation by 300 to isolate the exponential term.

2700/300=2(10*x)

9=2(10*x)

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

ln(9)=ln(2(10*x))

3. Use the power rule for logarithms, which states ln(ab)=b*ln(a) to bring the exponent down.

ln(9)=10*x*ln(2)

4. Isolate x by dividing both sides by 10*ln(2)

x=ln(9)/(10*ln(2))

5. Simplify the expression using the property ln(9)=ln(3)=2*ln(3)

x=(2*ln(3))/(10*ln(2))

x=ln(3)/(5*ln(2))

Final Answer

x=ln(3)/(5*ln(2))

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