The voltage in an electrical circuit is multiplied by itself each time it is reduced. The voltage is 27/125 of a volt and it has been reduced three times. Write the voltage in exponential form. What was the original voltage in the circuit?
Answer:
The exponential form of voltage [tex]x^{3} =\frac{27}{125}[/tex]
The original voltage in the circuit [tex]x=\frac{3}{5}[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the original voltage.
Given.
Three times reduced voltage is [tex]\frac{27}{125}[/tex]
And it is multiplied by itself each time when it is reduced, this gives us
[tex]x\times x\times x=x^{3}[/tex]
So the exponential form of voltage is
[tex]x^{3} = \frac{27}{125}[/tex]
Solve this equation for original voltage.
[tex]x^{3} = \frac{27}{125}[/tex]
[tex]x = (\frac{27}{125})^{\frac{1}{3}}[/tex]
[tex]x=\frac{\sqrt[3]{27} }{\sqrt[3]{125} }[/tex]
[tex]x=\frac{\sqrt[3]{3\times3\times3}}{\sqrt[5]{5\times5\times5}}[/tex]
[tex]x=\frac{3}{5}[/tex]
And Original voltage is [tex]x=\frac{3}{5}[/tex]
