KnowledgeBoat Logo
|

Mathematics

Find xx, if:

32x−1=(27)x−33^{2x-1} = (27)^{x-3}

Exponents

4 Likes

Answer

32x−1=(27)x−3⇒32x−1=(33)x−3⇒32x−1=(3)3(x−3)⇒32x−1=(3)3x−9⇒2x−1=3x−9⇒2x−3x=−9+1⇒−x=−8⇒x=83^{2x-1} = (27)^{x-3}\\[1em] \Rightarrow 3^{2x-1} = (3^3)^{x-3}\\[1em] \Rightarrow 3^{2x-1} = (3)^{3(x-3)}\\[1em] \Rightarrow 3^{2x-1} = (3)^{3x-9}\\[1em] \Rightarrow 2x - 1 = 3x - 9\\[1em] \Rightarrow 2x - 3x = -9 + 1\\[1em] \Rightarrow -x = -8\\[1em] \Rightarrow x = 8

If 32x−1=(27)x−33^{2x-1} = (27)^{x-3}, then x=8x = 8.

Answered By

3 Likes

Related Questions