Solving an exponential equation with a fraction as the exponent

👉 Learn about solving exponential equations. Exponential equations are equations involving exponents. To solve an exponential equation, we express the terms in both sides of the equality sign as single terms. Then, we express the single terms on both sides of the equality sign as powers having the same base. Once, we have expressed the terms as powers of the same base, we can then equate the exponents and hence solve for the unknown variable.

If the terms at both sides of the equality sign cannot be expressed as powers of the same base, then the logarithm of both sides of the inequality sign is taken and with our knowledge of logarithm laws/properties, we can solve for the unknown variable.

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✅Solve Exponential Equations with Logarithms
✅Solve Exponential Equations without a Calculator

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[tropicocean]

I think it's easier to use the property of same base. You rewrite .20 as 5^(-1) and set the exponents equal to each other
-t/2 = -1
Times (-2) gives you the answer of t=2

[joj]

is it possible to solve this particular equation without using log?

[balajishankar]

Sir, have a question. Can I not take log base 10 on both sides and then use the property log (m raised to n) base 10 = n * log m base 10.

-t/2 log 5 base 10 = log .20 base 10. It's easy to solve now with a calculator.

[ChavoMysterio]

5^(-t/2)=0.2
5^(-t/2)=5^-1
-t/2=-1
2(-t/2)=2(-1)
-t=-2
t=2 solution