Solving Exponential Equations with the Different Bases - Concept

Concept Concept (1)

Sometimes we are given exponential equations with different bases on the terms. In order to solve these equations we must know logarithms and how to use them with exponentiation. We can access variables within an exponent in exponential equations with different bases by using logarithms and the power rule of logarithms to get rid of the base and have just the exponent.

Sample Sample Problems (8)

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Solving Exponential Equations with the Different Bases - Problem 1

Solve:

5-t + 1 = 13
Problem 1
Solving an exponential equation with negative exponents by taking the common log of both sides.
Solving Exponential Equations with the Different Bases - Problem 2

Solve:

e0.04x = 18
Problem 2
Solving an exponential equation by taking the natural log of both sides.
Solving Exponential Equations with the Different Bases - Problem 3

Solve:

10x + 1 = 8
Problem 3
Solving an exponential equation by taking the common log of both sides.
Solving Exponential Equations with the Different Bases - Problem 4

Solve:

7x + 1 = 9x − 4
Problem 4
Solving an exponential equation by taking the common log of both sides and then factoring to obtain an answer.
Solving Exponential Equations with the Different Bases - Problem 5
Problem 5
Different methods of solving exponential equations with different bases
Solving Exponential Equations with the Different Bases - Problem 6
Problem 6
How to solve exponential equations with different bases that can not be rewritten as the same base.
Solving Exponential Equations with the Different Bases - Problem 7
Problem 7
How to solve for x in an exponent by two methods
Solving Exponential Equations with the Different Bases - Problem 8
Problem 8
How to solve logarithmic equations with two different bases and x in two separate exponents.