Solving an equation involving log_(10) If log_(10)(x) log_(10)(2) = 2 What is x ?

Nayeli Osborne

Nayeli Osborne

Answered question

2022-10-26

Solving an equation involving log 10
If
log 10 ( x ) log 10 ( 2 ) = 2
What is x ?
WolframAlpha says x = e 2 log 10 ( 2 )
But i don't understand why it is.. Please explain it. Thanks

Answer & Explanation

honotMornne

honotMornne

Beginner2022-10-27Added 12 answers

There's really not much to it, but you probably used ln when asking W|A (log is interpreted as the natural logaritm by default).
log 10 x log 10 2 = 2 log 10 x = 2 log 10 2 x = 10 log 10 x = 10 2 log 10 2
Oscar Burton

Oscar Burton

Beginner2022-10-28Added 3 answers

That's because, when you write down log in WolframAlpha, it is interpreted as log e or ln. So WolframAlpha solved the equation
ln ( x ) ln ( 2 ) = 2
Which is solved by first dividing the equation by ln 2, obtaining
l n ( x ) = 2 ln 2
Then using the fact that a = b e a = e b to get
( x = ) e ln x = e 2 ln 2

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