In Exercises 93–102, solve each equation. 3^x+2 ⋅ 3^x=81

Question

Accepted Answer

Welcome back. I am so glad you're here. We are given this equation five raised to the X plus one times five raised to the three X equals 125 and we are to solve for X. And we've got X up here in the exponents. So how do we get it out of there? Well let's see if we can do any simplification. First we look at these two terms being multiplied by each other and they have the same base five. And we know from previous lessons that rules for exponents tell us that when we have the same base that of two terms that are being multiplied, then their exponents are going to be added together. So we are going to add X plus one plus three X. So that would look like five raised to the X plus one plus three X. And that equals 125. Let's combine our like terms up here in the exponent X plus three X gives us five raised to the four, X plus one equals okay 125. Can that be converted to an exponents with a base of five? And yes it can. Five cubed equals 125. And now we've got the same base on both sides. And so five raise to the whatever it is here on the left with the X. In it is the same as five raised to the third. Or in other words these exponents are equal to each other. So now we can write that four X plus one equals three. And we can solve for X here, let's subtract one from both sides. So now we've got four X equals two. Let's divide both sides by four and we've got X equals one half. Or because all of our answers here are in decimals 0.5. We look at our answer choices in this matches with answer choice C. Well done, we'll catch you on the next one.

In Exercises 93–102, solve each equation. 3^x+2 ⋅ 3^x=81

Key Concepts

Exponential Equations

Properties of Exponents

Logarithms

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