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How do you find the inverse of #y=log(x+4)#?

Answer 1

To find the inverse of the function ( y = \log(x + 4) ), we first switch the roles of ( x ) and ( y ) and then solve for ( y ):

Replace ( y ) with ( x ) and ( x ) with ( y ): ( x = \log(y + 4) ).
Rewrite the equation in exponential form: ( 10^x = y + 4 ).
Subtract 4 from both sides to isolate ( y ): ( y = 10^x - 4 ).

Therefore, the inverse of ( y = \log(x + 4) ) is ( y = 10^x - 4 ).

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Answer 2

Benjamin Achtenberg

#y=10^x-4#

Flip the #x# and #y#.

#x=log(y+4)#

We want to solve for #y#. Remember that #log(y+4)# can also be written as #log_10(y+4)#.

#x=log_10(y+4)#

#10^x=10^(log_10(y+4))#

#10^x=y+4#

#y=10^x-4#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.