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Need Answer NOW!!! Solve for the following equation step by step and justify your steps when using an exponential property.

Need Answer NOW!!! Solve for the following equation step by step and justify your-example-1
User Rom Eh
by
8.1k points

2 Answers

4 votes

Answer:

x = 5/7

Explanation:

(7^x)^4) = 7^2 * 7^3 / 7^3x

1. Simplify the expression

(7^x)^4) becomes 7^4x

7^2 * 7^3 becomes 7^5

7^5/7^3x becomes 7^5 - 7^3x

Your new equation: 7^4x = 7^5 - 7^3x

2. Since the bases(7) are the same set the exponents equal to each other

4x = 5 - 3x

3. Combine like terms

4x + 3x = 5

7x = 5

4. Divide both sides by 7 to get x by itself

x = 5/7

User Macnique
by
7.8k points
2 votes

Answer:

x =
(5)/(7)

Explanation:


(7^(x))^(4)=(7^(2)* 7^(3))/(7^(3x))


(7^(x))^(4)=(7^((2+3)))/(7^(3x)) [Since
a^(b)* a^(c)=a^(b+c) ]


7^(4x)=(7^(5))/(7^(3x)) [since
(a^(b))^(c)=a^(bc) ]


7^(4x)={7^(5)*{7^(-3x)} [
(1)/(a)=a^(-1) ]


7^(4x)=7^((5-3x))

4x = 5 - 3x


4x+3x=5 ⇒ 7x = 5

x =
(5)/(7)

User Teastburn
by
8.5k points

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