# Log Prove

Discussion in 'Other Pre-University Math' started by nycmathguy, Nov 6, 2021.

1. ### nycmathguy

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nycmathguy, Nov 6, 2021

2. ### MathLover1

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log(b,((sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)))=2log(b(sqrt(3)+sqrt(2))

log(b,((sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)))

=>(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))........rationalize, multiply (sqrt(3)+sqrt(2))

=((sqrt(3)+sqrt(2))((sqrt(3)+sqrt(2))))/((sqrt(3) - sqrt(2))(sqrt(3)+sqrt(2)))

=(((sqrt(3)+sqrt(2))^2)/((sqrt(3) )^2- (sqrt(2))^2))

=((sqrt(3)+sqrt(2))^2)/(3- 2)

=((sqrt(3)+sqrt(2))^2)/1

=(sqrt(3)+sqrt(2))^2

then

log(b,(sqrt(3)+sqrt(2))^2 =2log(b,(sqrt(3)+sqrt(2))->proven

MathLover1, Nov 7, 2021
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3. ### nycmathguy

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nycmathguy, Nov 7, 2021
4. ### MathLover1

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manipulate left side

=> rationalize, , multiply by

=

=

=

=

=

substitute in log

=->proven

MathLover1, Nov 7, 2021
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5. ### nycmathguy

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1. Is this LaTex?

2. If not LaTex, what app did you use to type this reply?

3. Reply using this style of writing from now on. It's a lot easier to read and understand.

nycmathguy, Nov 7, 2021
6. ### MathLover1

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it's wolframalpha

MathLover1, Nov 7, 2021
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