I'll teach you how to solve 3ˣ⁺¹ = 9ˣ⁻²
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3ˣ⁺¹ = 9ˣ⁻²
Convert 9^x-2 to base 3:
3^x+1=(3^2)^x-2
Apply exponent rule:
3^x+1=3^2(x-2)
x+1=2(x-2)
Solve x+1=2(x-2):
Expand 2(x-2):
x+1=2x-4
Subtract 1 from both sides:
x+1-1=2x-4-1
Simplify:
x=2x-5
Subtract 2x from both sides:
x-2x=2x-5-2x
Simplify:
-x=-5
Divide both sides by -1:
-x/-1=-5/-1
Simplify:
x=5
Your Answer Is x=5
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