Question Video: Simplifying Algebraic Expressions Using Laws of Logarithms | Nagwa Question Video: Simplifying Algebraic Expressions Using Laws of Logarithms | Nagwa

# Question Video: Simplifying Algebraic Expressions Using Laws of Logarithms Mathematics • Second Year of Secondary School

## Join Nagwa Classes

Simplify log_(π₯) of the sixth root of π₯β΄.

01:51

### Video Transcript

Simplify log base π₯ of the sixth root of π₯ to the fourth power.

Before we do any simplification with the log, letβs think about simplifying this exponent. We know that the πth root of π₯ is equal to π₯ to the one over π power, which means we can rewrite this to say log base π₯ of π₯ to the fourth power to the one-sixth power. In this case, weβre taking a power of a power. And we can simplify π₯ to the π power to the π power by saying π₯ to the π times π power so that we have log base π₯ of π₯ to the four-sixths power. And this is where weβll need a log rule.

If we have log of π₯ to the π power, it will be equal to π times the log of π₯. This means we now have four-sixths times log base π₯ of π₯. But what is this saying, log base π₯ of π₯? Itβs asking us, π₯ to the what power would be equal to π₯? We know π₯ to the first power equals π₯. And this is where we get the rule that the log base π of π equals one. And that means we substitute one for log base π₯ of π₯, which gives us four-sixths times one.

Our instructions told us to simplify. And we havenβt simplified this expression completely because four and six are both divisible by two. If we divide the numerator and the denominator by two, we get two-thirds, which tells us that the log base π₯ of the sixth root of π₯ to the fourth power is two-thirds.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions