Question

Plz see attachment below

Answer 1

Explanation:

Table I

Given function is,

f(x) =
`b^x`

From the table attached,

For x = 0.827, value of function f(0.827) = 5,

f(0.827) =
`b^(0.827)`

Therefore,
`b^(0.827)=5`

`\text{log}(b^(0.827))=\text{log}(5)`

0.827[log(b)] = log(5)

log(b) = 0.8452

b =
`10^(0.8452)`

b = 7

Therefore, function 'f' will be,

f(x) =
`7^x`

For f(x) = 9,

9 =
`7^x`

log(9) = log(
`7^x`)

log(9) = x[log(7)]

x = 1.129

Table II

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

From the given table,

For x = 7, g(x) = 1

1 =
`\text{log}_b(7)`

`b^1=7`

b = 7

Therefore, the function 'g' will be,

g(x) =
`\text{log}_7(x)`

For g(x) = 1.318

1.318 =
`\text{log}_7(x)`

`x=7^(1.318)`

`x=12.9968`

`x=13.997`