Solve for 2y given exponential equation

MathematicsExponential EquationsEasy

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$6^x + 6^y = 42$

$x = 2$

$2y = ?$

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Step by Step Written Solution

1
Step 1

Hi Bengü, let's solve this together. We are given an equation with exponential terms and the value of one variable, and we need to find twice the value of the other variable.

Problem Summary

$$6^x + 6^y = 42$$
$$x = 2$$
$$2y = ?$$
2
Step 2

Let's start by substituting the given value of x, which is two, into our main equation.

Step 1: Substitution

$$6^x + 6^y = 42$$
$$x = 2$$
3
Step 3

Replacing x with two, we get six squared plus six to the power of y equals forty-two.

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Step 4

Now, let's calculate six squared. Since six times six is thirty-six, we can rewrite the equation.

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Step 5

Next, we need to isolate the term with y. Let's subtract thirty-six from both sides of the equation.

6
Step 6

Subtracting thirty-six from forty-two leaves us with six. So, six to the power of y equals six.

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About This Question

Subject
Mathematics
Topic
Exponential Equations
Difficulty
Easy
Question Type
Open Ended

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