Question Video: Solving a Logarithmic Equation | Nagwa Question Video: Solving a Logarithmic Equation | Nagwa

# Question Video: Solving a Logarithmic Equation Mathematics • Second Year of Secondary School

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Given that logββ (π£ + 3) = 1, find the value of π£.

01:18

### Video Transcript

Given that the log base 12 of π£ plus three equals one, find the value of π£.

Letβs consider this in two different ways. The first way is to rewrite this log in exponential form. If we know that log base π of π₯ equals π, then we can rewrite that as π to the π power equals π₯. For us, that will be 12 to the first power equals π£ plus three. We know that 12 to the first power equals 12. So we subtract three from both sides of the equation. And we see that nine equals π£ or more commonly π£ equals nine.

But is there another way we can think about this question? Well, if we know that log base π of π equals one, we could rewrite one in the form log base 12 of 12, since log base 12 of 12 does equal one. And then since weβre dealing with two logs with the same base, set equal to each other, we can say that π£ plus three is equal to 12. And again, weβll subtract three from both sides, to see that π£ equals nine. Both methods are valid ways to rearrange the equation to solve for π£.

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