[8/27]^x-1= [9/4]^2x+1 find the value of x
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2³ˣ⁺² = 3⁴ˣ⁺²
3³ˣ⁺² 2⁴ˣ⁺²
(2³ˣ ⁺²) (2⁴ˣ⁺²) = ( 3⁴ˣ⁺² ) (3³ˣ⁺²)
2⁷ˣ⁺⁴ = 3⁷ˣ⁺⁴
(2/3)⁷ˣ⁺⁴
7x + 4 = 0
7x = ⁻4
x = ⁻4/7
Anonymous:
Wth!! Wrong solution
Answered by
1
Answer:
x=1/7
Step-by-step explanation:
(8/27)^x-1=(9/4)^2x+1
as we know 8=2³,27=3³,9=3² and 4=2²
substituting the squares and cubes,
we get,
(2/3)^3x-3 = (3/2)^4x+2
-> as we know a^x=1/a^-x
we shift RHS upside-down so,
we get,
RHS=(2/3)^-4x-2
since both the bases of LHS and RHS are equal,
3x-3= -4x-2
the final answer will be x=1/7
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