Respuesta :
The inverse of given function is 1/[tex]5^x[/tex],last step in logarithmic equation is replace the new y with f⁻¹(x), the first thing I do to solve the exponential function is check whether function is one-to-one or not.
Steps involved in finding the inverse function are:
- Ensure your capability is one-to-one. Only coordinated capabilities have inverses.
- Given a capability, switch the x's and the y's.
- Recollect that f(x) subs for "y. Solve for the new "y.
- Replace the new "y" with f⁻¹(x)
We have function F(x)= [tex]log_5(x)[/tex]
Since, Logarithmic function are defined for positive values of x, so their domain is (0,inf),
For each value of x, we get unique value. Therefore its range is defined in [0,inf).
Since domain and range are on same interval. So, we can say that the given function is one-to one.
We need to find the inverse function, we need to equate the function with any variable like y.
=>y= [tex]log_5(x)[/tex]
=>[tex]5^y[/tex] =x
=>1/x=1/ [tex]5^y[/tex]
=>x⁻¹=1/ [tex]5^y[/tex]
Changing the variables, we get
=>y⁻¹=1/[tex]5^x[/tex]
Hence, inverse of given function is 1/[tex]5^x[/tex].
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(Complete question) is:
Write the inverse function of [tex]log_5(x)[/tex]? what is last step for solving a logarithmic equation? . what is the first thing you do to solve the given exponential equation?
