# Question Video: Solving Logarithmic Equations Mathematics • 10th Grade

Find π₯ such that log (4π₯ β 4) = 2.

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### Video Transcript

Find π₯ such that log of four π₯ minus four is equal to two.

Letβs write down the equation again. What is the base of this logarithm? When there isnβt a small subscript number next to the log, itβs a logarithm base 10.

We can write in this base explicitly if we want to. But you should always remember that a log without a base written explicitly means a log base 10.

Recall that the equation log base π of π equals π, which is in logarithmic form, is equivalent to the equation π to the power of π equals π, which is in exponential form. Letβs rewrite the equation we have to solve in exponential form.

Comparing to the general rule we see that π is 10. And so our equation is going to be 10 to the power of π equals π. π is four π₯ minus four. So we have that 10 to the power of π equals four π₯ minus four. And finally π is two. So we have 10 to the power of two is four π₯ minus four.

We give our focus to the equation in exponential form. We know whatβs 10 to the power of two is. Itβs 100. And so we have the equation 100 equal four π₯ minus four. This is now a linear equation that we know how to solve.

We add four to both sides and then divide by four to find that 26 equals π₯. And so π₯ equals 26. Our answer, therefore, the value of π₯ such that the log of four π₯ minus four is equal to two is 26.