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varshamittal029

The logarithmic form of the equation is [tex]log_{3}243=5[/tex] .

  • In mathematics, the logarithmic function is the inverse of power. Then the function is given as  f(x) = log x
  • The logarithm base  is a. This can be read  as the logarithmic base a of x. The two most  common bases used in logarithmic functions are base 10 and base e.
  • The logarithm function has several properties that allow the logarithm to be simplified when the input is in the form of products, quotients, or values ​​raised to powers.

We have given an equation 243 = 3⁵ .

Taking log on both sides , we get

   [tex]log(243) =log3^5[/tex]                    ..(1)

Applying the property of logarithm which is given by [tex]loga^b=bloga[/tex] in equation (1) ,we get

        [tex]log(243) =5log3[/tex]

On rearranging the above equation , we get

         [tex]\frac{log243}{log3} =5[/tex]                          ..(2)

Applying the property of logarithm which is given by [tex]log_xy=\frac{log_ay}{log_ax}[/tex]\

  [tex]\frac{log243}{log3}[/tex]   can be written as  [tex]log_{3}243[/tex] using property

Putting in equation (2) , we get

     [tex]log_{3}243=5[/tex]

Learn more about logarithmic form here :

https://brainly.com/question/13845508

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