Question

Using the graph of f(x) = log10x below, approximate the value of y in the equation 10^y = 3.

Answer 1

y=0.4771

Explanation:

Given : Using the graph of
`f(x) = \log_(10)x`

To find : The value of y in the equation
`10^y = 3` .

Solution :

Let,
`y= \log_(10)x`

and
`10^y = 3`

Now, we plot these two equations.

The graph of
`y= \log_(10)x` is shown with violet line.

The graph of
`10^y = 3` is shown with black line.

The solution to this system will be their intersection point.

The intersection point of these graph is (3,0.4771)

Refer the attached graph below.

Therefore, The value of y=0.4771

or we can verify it by,

`10^y = 3`

Taking log both side,

`y=\log_(10)3=0.4771`

Answer 2

Assuming log10x means log(base 10)x

Let's rewrite 10^y = 3 by taking the log(base 10) of both sides
log (10^y) = log (3) Remember that log(10^y) = y
y = log (3)
This is the same as our function f(x) = log(x), or f(3) = log(3)
Consult our graph of f(x) to find the y value at x=3
Checking the graph, we can find the value of y at point x=3
The value is .477. Therefore, y =.477, or about 1/2