If loga x=loga 6, then x=

Name: Problem 8, Chapter 5: Precalculus
Uploaded: 2020-07-05T19:47:59-08:00
Duration: 13 s
Channel: Kristen Karbon
Description: If loga x=loga 6, then x=

step 1 In order for the log base A of X to equal the log base A of 6, the arguments have to be the same

Question

$$\text { If } \log _{a} x=\log _{a} 6, \text { then } x=$$___

   $$\text { If } \log _{a} x=\log _{a} 6, \text { then } x=$$___

Precalculus

Michael Sullivan 9th Edition

Chapter 5, Problem 8

Instant Answer

Solved by Expert Kristen Karbon

07/05/2020

Step 1

Step 1: We are given that $\log _{a} x=\log _{a} 6$. Show more…

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$$\text { If } \log _{a} x=\log _{a} 6, \text { then } x=$$___

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Key Concepts

Equating the Arguments

When the logarithms on both sides of an equation have the same base, their arguments can be directly equated due to the one-to-one nature of logarithmic functions. This technique simplifies the process of solving the equation by turning it into a straightforward algebraic equation.

One-to-One Property of Logarithmic Functions

For any logarithmic function with a valid base (a > 0, a ? 1), the function is one-to-one. This means if log_a(x) equals log_a(y), then x must equal y. This property is fundamental when solving equations where logarithms on both sides share the same base.

Properties of Logarithms

Logarithms are the inverse operations of exponentiation, relating exponents to their corresponding bases and results. Understanding these properties is crucial when manipulating and solving logarithmic expressions and equations.

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