Question

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

Answer 1

y ≈ 0.01

y ≈ 1.48

y ≈ −2.01

y ≈ 0.78

Answer 2

@Hero @jim_thompson5910

Answer 3

The function is \[\Large f(x) = \log_{10}(x)\] right?

Answer 4

Yep

Answer 5

Replace f(x) with y. Then convert to exponential form.
\[\Large f(x) = \log_{10}(x)\]
\[\Large y = \log_{10}(x)\]
\[\Large 10^{y} = x\]

Answer 6

Then on the right side, replace x with 3 to get

\[\Large 10^{y} = 3\]

Answer 7

After all that, convert back to logarithmic form

\[\Large 10^{y} = 3\]
\[\Large y = \log_{10}(3)\]

Answer 8

So what you need to do is use the graph to find the y coordinate of the point on the curve when x = 3

Answer 9

Ok

Answer 10

what is that y value?

Answer 11

0.48?

Answer 12

That's not a choice though.

Answer 13

Alternatively, another approach is to realize that

\(10^0 = 1\)
\(10^1 = 10\)

So that means the value of y must be \(0 < y < 1\)

Answer 14

From this information you can easily eliminate the middle two options.

Answer 15

Actually, option 2 might be a typo

Answer 16

Ok, what I was doing earlier was plugging the choices into log(10)y. The closest I got was 0.01 = y and that disproved 10^y=3.

Answer 17

Option 2? What do you think is the alternative?

Answer 18

\(y \approx 0.48\)

Answer 19

Or the typo could be in option 4

Answer 20

I don't know which one, but if I had to pick, I'd choose option 2

Answer 21

Talk to your teacher about it.

Answer 22

That would make a lot of sense. I copied the answers over here correctly, but perhaps my source/test has an error.

Answer 23

Your test?

Answer 24

Assignment. Any way, she is unreachable today, so I'll just wing it. Thank you for your help.