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3 years ago

2. Solve 3^4x-5 = (1/27)^2x+10 for x. Show your work

Mathematics

1 answer:

Jlenok [28]3 years ago

6 0

It looks like the equation is supposed to read

3⁴ˣ ⁻ ⁵ = (1/27)²ˣ ⁺ ¹⁰

Recall that 3³ = 27, so 1/27 = 3⁻³ :

3⁴ˣ ⁻ ⁵ = (3⁻³)²ˣ ⁺ ¹⁰

Distribute the exponent on the right side:

3⁴ˣ ⁻ ⁵ = 3 ⁻⁶ˣ ⁻ ³⁰

The exponents must be equal for this equation to hold, so

4x - 5 = -6x - 30

Solve for x :

10x = -25

x = -25/10 = -5/2

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Work Shown:

Start at point A' and count how many spaces it takes to get to E'. You should count out 6 spaces. This means A'E' = 6

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3 years ago