Question

Match the y-coordinate with the given x-coordinate for the equation y = log10x.

Answer 1

1. log {10 (1/100) } = log {1/10} = -1

2. log {10 (1/10)} = lg {1} = 0

3. log {10 (1)} = lg (10) = 1

4. log {10 (10)} = log {100} = 2

5. log {10 (100)} = log{1000} = 3

Answer 2

The non-algebraic functions are called transcendental functions. This include the logarithmic function. The definition of Logarithmic Function with Base a is as follows:

$For \ x\ \textgreater \ 0, \ a \ \textgreater \ 0, \ and \ a \neq 1 \\ \\ y=log_{a}x \ if \ and \ only \ if \ x=a^{y} \\ \\ Then: \\ \\ f(x)=log_{a}x \\ \\ is \ called \ the \ logarithmic \ function \ with \ base \ a.$

We know that the equations is:

$y=log(10x)$

So let's solve each case:

Case 1

$x=\frac{1}{100} \\ \\ y=log(10(\frac{1}{100})) \\ \\ \therefore y=log(\frac{1}{10}) \\ \\ \therefore y=-1 \\ \\ So: \\ \\ \boxed{\ x=\frac{1}{100}} \ matches \ to \ \boxed{y=-1}$

Case 2

$x=\frac{1}{10} \\ \\ y=log(10(\frac{1}{10})) \\ \\ \therefore y=log(1) \\ \\ \therefore y=0 \\ \\ So: \\ \\ \boxed{\ x=\frac{1}{10}} \ matches \ to \ \boxed{y=0}$

Case 3

$x=1 \\ \\ y=log(10(1)) \\ \\ \therefore y=log(10) \\ \\ \therefore y=1 \\ \\ So: \\ \\ \boxed{\ x=1} \ matches \ to \ \boxed{y=1}$

Case 4

$x=10 \\ \\ y=log(10(10)) \\ \\ \therefore y=log(100) \\ \\ \therefore y=2 \\ \\ So: \\ \\ \boxed{\ x=10} \ matches \ to \ \boxed{y=2}$

Case 5

$x=100 \\ \\ y=log(10(100)) \\ \\ \therefore y=log(1000) \\ \\ \therefore y=3 \\ \\ So: \\ \\ \boxed{x=100} \ matches \ to \ \boxed{y=3}$