Exponential function can be defined as Functions which have power with variables. These powers with variables are called as exponents. In other words, variable or number that we will be raising to a power is known as base and power is referred as exponent. Exponents can be solved in both situations when bases are same and when bases are different. Let’s understand how to solve exponents with different bases? Exponential functions with different bases can be calculated using common factor property. Using this property, it is possible to get exponential with same base. In second method, base of Logarithm term will be ‘e’. One of the Properties of Logarithms
shows that if there is an exponential term existing then put this exponent ahead of log term. It can be expressed as shown below:
log b (a)x = x * log b (a).
Following steps can be used solve exponents with different bases:
1) First of all, take Logarithm of base on both sides of equation.
2) Bring the exponent down using property log b (a) y = y * log b (a).
3) Solve for ‘y’.
Let’s take an example 9 y = 4
First of all, take ln (log e) on both sides, we get:
ln (9y) = ln 4.
Above equation can be written as: y * l n (9) = l n (4),
Divide both sides by l n (9) to get "y". So y = l n (4) / l n (9)
This equation can further be solved by substituting values of log e (4) and log e (9).