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Banguizb 2022-07-08 Answered
It's a logarithmic worksheet and O can't solve it.
log a x = p, log b x = q , log a b c x=r. What is log c x?.. It's on my math homework can someone solve it cause I need it.
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Answers (2)

lydalaszq
Answered 2022-07-09 Author has 11 answers
So, use the log change of basis formula:
log ( x ) / log ( a ) = p log ( x ) / log ( b ) = q log ( x ) / log ( a b c ) = ( log ( a ) + log ( b ) + log ( c ) log ( x ) ) 1 = r
and so log ( x ) / log ( c ) = ( log ( c ) log ( x ) ) 1 = ( log ( a ) + log ( b ) + log ( c ) log ( x ) log ( b ) log ( x ) log ( a ) log ( x ) ) 1 = ( 1 r 1 q 1 p ) 1

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pouzdrotf
Answered 2022-07-10 Author has 4 answers
Using
Change of Base Formula:
log a x = log b x log b a
And Product:
log a ( x y ) = log a x + log a y
And
log a a = 1
You have:
log a b c x = l o g x x log x a b c = 1 log x a b c = r
log a x = log x x log x a = 1 log x a = p log x a = 1 p
log b x = log x x log x b = 1 log x b = q log x b = 1 q
So substituting what you have from above:
1 log x a b c = 1 log x a + log x b + log x c = 1 1 p + 1 q + log x c = r
1 = r ( 1 p + 1 q + log x c )
1 r p r q r = log x c
Following from above
log c x = 1 log x c = 1 1 r p r q r = 1 1 r 1 p 1 q
Can also be expressed as
( 1 r 1 p 1 q ) 1

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