Question

Which table represents the graph of a logarithmic function in the form y=log3x when b>1?

Answer 1

Answer:

The satisfied table of the given function$y = log_{b} (x)$

x                    1/8            1/4             1/2              1             2

y                    -3                 -2            -1               0               1

Step-by-step explanation:

Explanation :-

Given logarithmic function $y = log_{b} (x)$   if b >1

Given first table

i)

put x = $\frac{1}{8}$     given b > 1 so we can choose b = 2

$y = log_{2} (\frac{1}{8} )$

$y = log_{2} (2^{-3} )$

we will apply logarithmic formula

log x ⁿ = n log (x)

$y = log_{2} (2^{-3} ) = -3 log_{2} (2) = -3 (1) = -3$

y = -3

ii)

put x = $\frac{1}{4}$     given b > 1 so we can choose b = 2

$y = log_{2} (\frac{1}{4} )$

$y = log_{2} (2^{-2} )$

we will apply logarithmic formula

log x ⁿ = n log (x)

$y = log_{2} (2^{-2} ) = -2 log_{2} (2) = -2 (1) = -2$

y = -2

iii)

put x = $\frac{1}{2}$     given b > 1 so we can choose b = 2

$y = log_{2} (\frac{1}{2} )$

$y = log_{2} (2^{-1} )$

we will apply logarithmic formula

log x ⁿ = n log (x)

$y = log_{2} (2^{-1} ) = -1 log_{2} (2) = - (1) = -1$

y = -1

iv)

put x = 1     given b > 1 so we can choose b = 2

$y = log_{2} (1 )$ = 0

y = 0

v)

put x = $2$     given b > 1 so we can choose b = 2

$y = log_{2} (2 )$

y = 1

Final answer:-

The satisfied table of the given function

x                    1/8            1/4             1/2              1             2

y                    -3                 -2            -1               0               1

Answer 2

Answer:

A just took it and got it right

Step-by-step explanation: