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listeningintently

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Logarithms

hello

Here's the question I need a hand with:

(log10x)(log10x²) + log10x³ - 5 = 0

And I need to solve for x

Thanks in advance

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Logarithms

Use y = log_10(x).

Then using laws of logs, your equation is equivalent to 2y² + 3y - 5 = 0.
Find the two values of y that solve this quadratic, then put them back in the substitution to get x.

(Only one value of y will be positive, which means only one real x exists. There's another complex one though, if you need to find that too.)

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Why did the vector cross the road?
It wanted to be normal.