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2 years ago

Solve for 'x' in the following equation, explaining each step. 3^ (-3x+7) = 3^ (7x-13)

Mathematics

1 answer:

Yanka [14]2 years ago

5 0

Answer:

x = 2

Step-by-step explanation:

In order to have the two sides of the equation be equal, the exponents must equal.

-3x + 7 = 7x - 13

Add 3x to both sides.

7 = 10x - 13

Add 13 to both sides.

20 = 10x

Divide by 10.

2 = x

Check:

3^(-3•2+7)=3^(7•2-13)

3^1 = 3^1

3 = 3

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2 years ago

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What values of a and b make the equation true? StartRoot 648 EndRoot = StartRoot 2 Superscript a Baseline times 3 Superscript b

kramer

Option C: $a=3, b=4$ is the value of a and b

Explanation:

Given that the expression $\sqrt{648}=\sqrt{2^a\times3^b}$

We need to determine the value of a and b

Let us consider the term $\sqrt{648}$ and take the prime factorization of the term 648

Thus, we have,

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$648=2 \cdot 324$

324 divides by 2,

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$\sqrt{648}=\sqrt{2^{3} \cdot 3^{4}}$

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3 years ago

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Answer:

Step-by-step explanation:

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