In Exercises 79–84, solve for y.
79. 3^y = 2^(y+1)

Question

In Exercises 79–84, solve for y.

79. 3^y = 2^(y+1)

Accepted Answer

Welcome back, everyone. Solve for Y 5 Y + 2 equals 7 of 2Y minus 1. Now, in this problem, let's understand that our unknown why is in the exponent of each term. So what we can do is simply apply the properties of logarithms and we can apply. The logarithm to both sides of this equation. What we're going to do is simply use the natural logarithm. So applying the natural logarithm we get LN of 5 power of Y + 2 is equal to LN of 7 of 2Y minus 1. And the reason why this is helpful. It is because we can apply the power rule of logarithms, so we can bring down each exponent and write it in front of the log. So we get Y + 2 multiplied by LN of 5 is equal to 2 Y minus 1 multiplied by LN of 7, and then we can solve for Y. Let's distribute. We get Y LN of 5 plus 2 LN of 5 is equal to. 2 of 7 minus Helen of 7. Now, let's label the Y terms, and let's ensure that we have Y terms on the same side of the equation. So we can subtract YLN of 5 from both sides to get to Y. LN of 7 minus Y LN of 5 equals and we can add LN of 7 to both sides. So we get 2 LN of 5 plus LN of 7. And now let's factor out Y. So we get Y in to LN of 7 minus LN of 5 equals. 2 LN of 5 plus LN of 7. And how to solve for Y, we're going to divide by the constant on the left hand side. So that's 2 LN of 5. Plus LN of 7. Divided by 2 LN of 7 minus LN of 5. And because this answer appears to be bulky, we can simplify using the properties of logarithms. So, since we have a sum of logarithms, and to apply the property of sum, we are going to apply the power rule as well. So 2 LN of 5 is LN of 5 squad, that's the power rule in reverse. Which is LN of 25, basically, we're adding LN of 7. So now what we can do is simply rewrite this sum as LN of 25 multiplied by. 7 And then we can apply the same properties in the denominator. We have LN of 7 squared, so that's LN of 49 minus LN of 5. In this case, we have difference, so we can apply the quotient rule. That would be Alan off. 49 divided by 5. So now simplifying we get LN of 175 divided by. LN of 49 divided by 5, which is our final answer for the value of Y. Thank you for watching.

In Exercises 79–84, solve for y.79. 3^y = 2^(y+1)

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In Exercises 79–84, solve for y.
79. 3^y = 2^(y+1)