Question

Solve the equation for $x$. $$6^{2 x}=6^{6}$$

   Solve the equation for $x$.
$$6^{2 x}=6^{6}$$

Applied Calculus for the MLSS A Brief Approach

Applied Calculus for the MLSS A Brief Approach

Soo T. Tan 10th Edition

Chapter 5, Problem 17

Instant Answer

Solved by Expert Priyanka Sadarangani

05/12/2021

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When the bases are the same, we can set the exponents equal to each other. Show more…

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Solve the equation for $x$. $$6^{2 x}=6^{6}$$

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Key Concepts

Exponential Functions

Exponential functions are mathematical functions in which a constant base is raised to a variable exponent. They are characterized by their rapid growth or decay and have the general form a^x, where a is a positive constant. These functions are widely used in modeling real-world phenomena such as population growth, radioactive decay, and interest calculations.

One-to-One Property of Exponential Functions

The one-to-one property of exponential functions states that if the bases of two exponential expressions are equal and positive (and not equal to one), then the equality of the expressions implies the equality of their exponents. This property is essential when solving exponential equations, as it allows you to equate the exponents directly when the bases are the same.

Solving Linear Equations

Solving linear equations involves isolating the variable by performing inverse operations such as division, multiplication, addition, or subtraction. In the context of the given problem, once the exponents are set equal to each other using the one-to-one property, the result is a linear equation in the variable, which can be solved straightforwardly to find its value.

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