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