Question

Please help me out with thissss

Answer 1

Explanation:

From table 1,

f(x) = bˣ

For x = -1,

f(-1) = 0.5

0.5 = (b)⁻¹

b =
`(1)/(0.5)`

b = 2

For x = 1.585,

f(1.585) = 3

3 =
`2^(1.585)`

3 =
`2^(1)*2^(0.585)`

`2^(0.585)=(3)/(2)`

`2^(0.585)=1.5`

For x = 2.585,

f(2.585) =
`2^(2.585)`

=
`2^(2)* 2^(0.585)`

= 4 × 1.5 [Since,
`2^(0.585)=1.5`]

= 6

From table 2,

g(x) =
`\text{log}_b(x)`

For x = 0.5,

g(0.5) = -1

-1 =
`\text{log}_b(0.5)`

b⁻¹ = 0.5

b = 2

For x = 2,

g(2) = 1

1 =
`\text{log}_2(2)`

For x = 6,

g(6) = 2.585

2.585 =
`\text{log}_2(6)`

2.585 =
`\text{log}_2(2* 3)`

2.585 =
`\text{log}_2(2)+\text{log}_2(3)`

2.858 - 1 =
`\text{log}_2(3)`

`\text{log}_2(3)=1.585`

For x = 3,

g(3) =
`\text{log}_2(3)`

g(3) = 1.585