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For the functions ƒ(x) = loga(x) and g(x) = logb(x), for what value(s) of x is ƒ(x) = g(x)?

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For the functions ƒ(x) = loga(x) and g(x) = logb(x), for what value(s) of is ƒ(x) = g(x)?

asked May 21, 2014 in PRECALCULUS by bilqis Pupil

1 Answer

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Change-of-Base Formula :

Let a, b, and x be positive real numbers such that a ≠ 1 and b ≠ 1. Then can be converted to a different base as follows.

image

The logarithm functions are .

The functions are equal, f(x) = g(x) and solve for x.

.

Changing Bases Using Common Logarithms:

image

image

image

Divide each side by image.

image

image      [ log(1) = 0 ]

Apply One - to - One property of logarithm : image.

x = 1.

The value of x = 1.

answered May 21, 2014 by steve Scholar

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