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How can exponential equations with unequal bases be solved?

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Solution:

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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.

User Litrik De Roy
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