Question

How can exponential equations with unequal bases be solved?

Answer 1

we have been asked to explain

How can exponential equations with unequal bases be solved?

So Suppose we have an example of exponential equations with unequal bases as

`a^x=b^(x-3)`

This can be solved by taking logarithm on both the sides we get

`Loga^x=Logb^(x-3)`

Using the Logarithmic exponent property we can write

`xLoga=(x-3)Logb`

`xLoga=xLogb-3Logb`

`x(Loga-Logb)-=-3Logb`

`x=(-3Logb)/(Loga-Logb)\\`

From here either we can simplify it further or we can substitute the values using calculator and on simplification we will get the final answer.

Hence we can solve using Logarithm.