Question

What is the solution to this equation?
9^x-1=2
A.2
B.-1/2
C.1/2
D.1

Answer 1

Option C) ½ is the correct answer.

Step-by-step Step-by-step explanation:

SOLUTION :

`\longrightarrow \sf{ {9}^(x) - 1=2}`

Taking 1 to RHS side :
`\longrightarrow \sf{ {9}^(x)=2 + 1}`

`\longrightarrow \sf{ {9}^(x) = 3}`

We can write 3 as 3¹

`\longrightarrow \sf{ {9}^(x) = {3}^(1)}`

We can write 9ˣ as (3²)ˣ

`\longrightarrow \sf{{({3}^(2))}^(x) = {3}^(1)}`

Using identity [(aᵐ)ⁿ = aᵐⁿ]

`\longrightarrow \sf{{3}^(2 * x)= {3}^(1)}`

`\longrightarrow \sf{{3}^(2x)= {3}^(1)}`

Dividing by 3 on both sides :

`\longrightarrow \sf{{ \cancel{3}}^(2x)= {\cancel{3}}^(1)}`

`\longrightarrow \sf{2x= 1}`

`\longrightarrow\boxed{\sf{x= (1)/(2)}}`

Hence, the value of x is 1/2.

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