Express lg &#x2061;<!-- ⁡ --> y x 2 </msup> </mfrac> in terms of

istremage8o

istremage8o

Answered question

2022-05-31

Express lg y x 2 in terms of a and b.
If lg x 2 y = a and lg x y = b,Express lg y x 2 in terms of a and b.
I did this, I don't know whether it right or wrong!
lg x 2 y = a can be written as: l g x 2 lg y = a
Then: lg x 2 = a lg y
and lg x y = b can be written as: lg y = b + lg x
As I'll have to express lg y x 2 , I made l g x 2 and lg y, so now I can substitute the values into l g y x 2
Is this the right way?
***If I continue in this way, the answer doesn't come right! :'( Help

Answer & Explanation

soymmernenx

soymmernenx

Beginner2022-06-01Added 10 answers

Careful!
log ( a b ) log a log b. Rather, log ( a b ) = log a + log b
So... log ( x 2 y ) = a log ( x 2 ) + log ( y ) = a 2 log x + log y = a
log ( x y ) = b does give us log y = log x b you are correct.
And we can express log ( y x 2 ) as
log y log ( x 2 ) = log ( y ) 2 log x
Aidyn Cox

Aidyn Cox

Beginner2022-06-02Added 5 answers

Your error was l g x 2 lg y = a

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