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Anastasy [175]
3 years ago
14

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

4<em>x</em> - 5 = -6<em>x</em> - 30

Solve for <em>x</em> :

10<em>x</em> = -25

<em>x</em> = -25/10 = -5/2

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