For the exponential fuction f(x)=10^x, find f(3/2)f(3/2)=?

ediculeN 2021-09-23 Answered

For the exponential fuction \(\displaystyle{f{{\left({x}\right)}}}={10}^{{x}}\), find \(\displaystyle f{{\left(\frac{3}{{2}}\right)}}\)
\(\displaystyle f{{\left(\frac{3}{{2}}\right)}}=?\)
Type an exact answer, using radicals as needed.

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Expert Answer

Ayesha Gomez
Answered 2021-09-24 Author has 10704 answers

First of all, put the value of \(\displaystyle{x}=\frac{3}{{2}}\) in \(f(x)\).
\(\displaystyle{f{{\left({x}\right)}}}={10}^{{x}}\)
\(\displaystyle{f{{\left({\frac{{{3}}}{{{2}}}}\right)}}}={10}^{{{\frac{{{3}}}{{{2}}}}}}\)
Now, use the radicals and simplify to find \(\displaystyle f{{\left(\frac{3}{{2}}\right)}}\).
\(\displaystyle{f{{\left({\frac{{{3}}}{{{2}}}}\right)}}}={10}^{{{\frac{{{3}}}{{{2}}}}}}\)
\(\sqrt[2]{10^3}\)
\(\displaystyle=\sqrt[2]{{10}\times{10}\times{10}}\)
\(\displaystyle{10}\times\sqrt[2]{10}\)
\(\displaystyle={10}\times{3.162}\)
\(\displaystyle{f{{\left({\frac{{{3}}}{{{2}}}}\right)}}}={31.62}\)

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