Question

Explain, in at least 3 steps, how to solve this exponential equation with unequal bases.

Answer 1

Explanation;

To solve an exponential Equation with different bases we need to the following steps;

1. Isolate the exponential part of the equation. If there are two exponential parts put one on each side of the equation.

2^x=3^x+1

2. Introduce logarithm of each side of the equation;

log 2^x = log 3^x+1

3. Then apply power property to rewrite the exponent.

x log 2= (x+1)log 3

4. Then Solve for the variable ;

x log 2 = log 3 + x log 3

x log 2 - x log 3 = log 3

x (log 2 - log 3) = log 3

and x = log 3 / (log 3 - log 2)