Divide both sides by 2: \(\displaystyle{5}^{{x}}+{3}={3125}\)

Write the right side using base \(\displaystyle{5}.{3125}={5}^{{5}}\) so: \(\displaystyle{5}{x}+{3}={5}^{{5}}\)

Equate exponents: \(x+3=5\)

Subtract 3 from both sides: \(x=2\)

Question

asked 2020-10-31

\(\displaystyle∫{\left(\frac{{{2}{x}^{{3}}}}{{{1}+{x}^{{4}}}}\right)}{\left.{d}{x}\right.}\)

asked 2021-01-07

solve the equation \(\displaystyle{4}{x}^{{3}}={324}\)

asked 2020-12-02

Write each of the numbers 1, 8, 27, 64, and 125 as a base raised to the third power.

\(\displaystyle{1}=⎕^{{3}}\)

\(\displaystyle{8}=⎕^{{3}}\)

\(\displaystyle{27}=⎕^{{3}}\)

\(\displaystyle{64}=⎕^{{3}}\)

\(\displaystyle{125}=⎕^{{3}}\)

\(\displaystyle{1}=⎕^{{3}}\)

\(\displaystyle{8}=⎕^{{3}}\)

\(\displaystyle{27}=⎕^{{3}}\)

\(\displaystyle{64}=⎕^{{3}}\)

\(\displaystyle{125}=⎕^{{3}}\)

asked 2020-12-25

Simplify the following. Write answers without negative exponnents.
\(\displaystyle{\left({4}{x}^{{2}}{y}^{{-{{3}}}}\right)}^{{-{{2}}}}\)