Question Video: Finding the Value of a Logarithm Using Substitution | Nagwa Question Video: Finding the Value of a Logarithm Using Substitution | Nagwa

# Question Video: Finding the Value of a Logarithm Using Substitution Mathematics • Second Year of Secondary School

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Given that the graph of the function π(π₯) = log_(π) π₯ passes through the point (1,024, 5), find the value of π.

02:07

### Video Transcript

Given that the graph of the function π of π₯ equals log to the base π of π₯ passes through the point 1024, five, find the value of π.

Well, what we have in this question is a function that is equal to log to the base π of π₯. So, what weβre gonna do is use some of the relationships we know about logarithms. Well, what we know about logarithms is that if we have π is equal to log to the base π of π, then what we can say is that π is gonna be equal to π to the power of π. So therefore, if we apply this to our function, what we can say is that the value of the function is π. Then, weβve got the base. Well, in our expression or our function, weβve got that itβs π. But if weβre looking at our relationship that weβve got down here, that would be our π and in fact the π₯ would be our π.

Well, now, what we can do is look at the fact that weβve got a point on our function, and that point is 1024, five. So, what we can do is use this to substitute in π₯- and π¦-values. Because using this information, what we can say is that five β because five is our π¦-value or the value of our function β is equal to log to the base π of 1024. And thatβs because this is our π₯-value. Okay, but what do we do now? Well, we want to find π, and we can do that using the relationship we showed you just now.

So, as weβd already identified from the π, π, and π that weβd shown in our general form for the relationship, weβve got our π which is 1024, our π is π, and our π is five. So therefore, we can rewrite our equation as 1024 is equal to π to the power of five. So then to find out what π is, what we can do is take the fifth root of both sides of the equation. And when we do that, weβre gonna get four is equal to π.

So therefore, we can say that given that the graph of the function π of π₯ equals log to the base π of π₯ passes through the point 1024, five, then the value of π is four.

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