Answer:
y=log_(6)x
Step-by-step explanation:
From the definition of logarithm:
[tex]x = log_b y[/tex] <---> [tex]y=b^x[/tex]
In our case, we have
[tex]y=6^x[/tex]
which means that b=6, therefore the inverse function is
[tex]x=log_6 y[/tex]
which can be rewritten by switching x and y:
[tex]y=log_6 x[/tex]
Logarithm helps to find the power to which a number must be raised to get the desired number. The inverse of y=6ˣ is log₆y = x.
A log function is a way to find how much a number must be raised in order to get the desired number.
[tex]a^c =b[/tex] can be written as [tex]\rm{log_ab=c[/tex]
where a is the base to which the power is to be raised,b is the desired number that we want when power is to be raised,c is the power that must be raised to a to get b.
For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.
[tex]\rm log_{10}1000 =3[/tex]
Given to us
y=6^x
We know the concept of the logarithm, therefore,
[tex]y=6^x\\\\6^x = y\\\\log_6y = x[/tex]
Hence, the inverse of y=6ˣ is log₆y = x.
Learn more about Logarithm:
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