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Combine the given expression into a single logarithm.$$1 / 2 \log _{6} 25+2 \log _{6} 3$$

$$\log _{6} 45$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Campbell University

McMaster University

Harvey Mudd College

Lectures

01:38

Rewrite each expression as…

01:02

Write logarithmic expressi…

01:44

Combine the given expressi…

00:25

Write each expression as t…

00:53

Write the logarithms as $a…

00:44

Write the logarithmic expr…

00:12

01:06

01:05

Condense the expression to…

01:09

$$\log _{3}\left[\log …

00:30

Write each logarithmic exp…

00:38

00:32

Use the Laws of Logarithms…

Simi Tech can. So in this problem, we have one half log based six of 25. And what we're gonna do is we're gonna undo the law of logs to simplify this to a single log, all basics of three. So the first thing and the order does matter that you want to start with the coefficients in front make them into exponents. So the things that were being multiplied in front s. So that means that we're equal to log based six of 25 to the one half power plus log based, six of three squared. All right. And then I imagine all students in calculus are pretty familiar that to the one half power means a square roots of the square root of 25. It's five. Okay. And then this three squared three times three is nine. But then the second law of logs that were going to use that when we are adding to logs with the same base, we can multiply these two numbers together. Bye. So our final answer I'll just write off to the side is log basic stays the same and five times nine s, 45. There's your answer

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