The non-algebraic functions are called transcendental functions. This include the logarithmic function. The definition of Logarithmic Function with Base a is as follows:
\(For \ x\ \textgreater \ 0, \ a \ \textgreater \ 0, \ and \ a
eq 1 \\ \\ y=log_{a}x \ if \ and \ only \ if \ x=a^{y} \\ \\ Then: \\ \\ f(x)=log_{a}x \\ \\ is \ called \ the \ logarithmic \ function \ with \ base \ a.\)
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
\(x=100 \\ \\ y=log(10(100)) \\ \\ \therefore y=log(1000) \\ \\ \therefore y=3 \\ \\ So: \\ \\ \boxed{x=100} \ matches \ to \ \boxed{y=3}\)
