Question

Which logarithmic graph can be used to approximate the value of y in the equation 3y = 8? The graph of function f of x equals log base 4 of x minus 4 The graph of function f of x equals log base 3 of x The graph of function f of x equals log base 4 of x The graph of function f of x equals log base 4 of x plus 3

Answer 1

So basically, you are looking for a base 3 log graph.

Steps:

Take the base 3 log on both sides of 3^y = 8 to get y = base 3 log 8.

To find the curve that is base three log 8, you should look at some points; in this case, the base 3 log 9=2, and base 3 log 3=1.

So, you should get a graph with points (1,0) (3,1) (9,2).

Therefore, based from what we got, the graph of function f of x equals log base 3 of x is the logarithmic graph that can be used to approximate the value of y in the equation 3y = 8.

Answer 2

The function is 3^y = 8

Then, you can apply base 3 logarithm to both sides.

That results in base:

base 3 log (3^y) = base 3 log (8)

And from that:

y * [base 3 log 3] = base 3 log (8)

using the property that base 3 log 3 = 1, you get:

y = base 3 log (8).

So, you can approximate the value of y using the function f(x) = base 3 log (x). Just look for the value of that function for x = 8.

That is the second option of the list: the graph of function f of x equals log base 3 of x.