# Question Video: Evaluating a Logarithmic Function at a Given Point Mathematics • 10th Grade

Consider the function π(π₯) = logβ (3π₯ β 1). If π(π) = 3, find the value of π.

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### Video Transcript

Consider the function π of π₯ is equal to log base two of three π₯ minus one. If π of π is equal to three, find the value of π.

We are told that π of π is equal to three, so we can begin by substituting these values into the function π of π₯. This gives us log base two of three π minus one is equal to three. We recall that logarithmic functions are the inverses of exponential functions. This means that if log base π of π¦ is equal to π₯, then π to the power of π₯ is equal to π¦. In this question, the base π is equal to two, the variable π¦ is equal to three π minus one, and the variable π₯ is equal to three. Two cubed is therefore equal to three π minus one.

We know that two cubed is equal to eight. We can then add one to both sides of this equation so that three π is equal to nine. Dividing both sides of this equation by three gives us π is equal to three. If the function π of π₯ is equal to log base two of three π₯ minus one and π of π is equal to three, then the value of π is three. We could check this answer on the calculator by substituting our value back in to the original function.