Simplifying Logarithms

Hi guys, its me Gurpreet again. Today we're gonna learn about simplifying logarithms, don't worry the process is really easy, and in fact you have already learnt this. Just take what you learnt from expanding logarithms and work backwards!!

Expanding Logarithm Rules:
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1. Roots become fractional exponents
2. Division becomes subtraction.
3. Multiplication become addition.
4. Exponents become coefficients.
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Simplifying Logarithm Rules:
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1. Move all negative terms to the end.
2. Coefficients become exponents.
3. Addition become multiplication.
4. Subtraction becomes division.
5. Fractional exponents become roots.
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All right, now lets try an example, Here's an expanded logarithm:

1/3log(x-1) - 4log(x+1) + log3

1. Step one is to move all negative terms/logs to the end:
1/3log(x-1) + log3 - 4log(x+1)


2. Step two is to turn all coefficients into exponents.
log(x-1)^1/3 + log3 - log(x+1)^4


3. Step three is to turn addition into multiplication.
log3(x-1)^1/3 - log(x+1)^4


4. Step four is to turn subtraction into division.
log3(x-1)^1/3 / (x+1)^4


5. Step five is to tun all fractional exponents into roots.
log3³√x-1 / (x+1)^4


There you are!! through these steps you have simplified the logarithm of
1/3log(x-1) - 4log(x+1) + log3 into log3³√x-1 / (x+1)^4
Just follow these steps and you can simplify any logarithm!!
Anyway, Im gonna go to sleep, hopefully I'll get some bonus marks for this! Good Night!