Solve each equation. 3x - 15 = log￬x 1 (x0, x≠1)

Question

Solve each equation. 3x - 15 = log￬x 1 (x>0, x≠1)

Accepted Answer

Solve the following logic equation for X log base X of one equals eight X minus 32 with domain restrictions of X being greater than zero and not equals to one possible solutions being 48 16 or six. Now, to solve this, we'll make use of a couple of properties. We have one X of one equals eight X minus which we can first make use of changing a log to an exponential. Now let's do that. We can look at Y equals log base A of X which is our log formula can rewrite it as X equals a race to the Y which is the equivalent exponential formula. If you look here, our base A will be equals X or X is one, er Y is eight X minus 32. We can then re write this as X raised to the index minus 32 equals one. Now he wants to get rid of the X as the base exponential to do that. We need exponentials with base X. On both sides, we can rewrite one as X to the zero. If you bring down our X to the eight X minus 32 we have the same base. We can then just bring down our exponentials eight X minus 32 equals zero. Then we could just solve for X at 32 of the both sides to get eight X equals 32. Finally divided by eight to get X equals four. Mean our solution set will just be four. If you look at our possible answers, our answer corresponds to answer A OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Solve each equation. 3x - 15 = log￬x 1 (x>0, x≠1)

Key Concepts

Logarithmic Functions

Properties of Logarithms

Solving Linear Equations

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