natural logs

[scarlet crystal]

how do you simplify this?

[deep scarab]

ln (8x)^1/2 - ln(16x)^1/2 = ln (1/2)^1/2

[crude egret]

^^^

[scarlet crystal]

umm I don't really get it did you transpose the ln(4x^2)

[deep scarab]

wait

[deep scarab]

this

ln(1/2)^1/2 + ln(4x^2)

so ln(1 / sqrt(2) * 4x^2)

so what is 1 / sqare root of 2) times 4x^2

you can break out a square root of 2 out of 4

to get

4 = 2 *sqrt(2) *sqrt(2)

so you divide away 1 sqrt(2)

and get

2 sqrt(2) times x^2

so final is

ln(2 times sqrt(2) times x^2)

[scarlet crystal]

Is that the same as

this is the answer given in the answer key, which I don't get

[deep scarab]

yes its the same

square root of 8

break out the 4

[scarlet crystal]

ah I see

[deep scarab]

square root of 4 is 2

square root of 2 is square root of 2

so sqaure root of 8 is 2 times square root of 2

then you just add the power 2 to the x

and multiply both expressions

so its the same

[scarlet crystal]

I don't get where this comes from

[deep scarab]

.

[deep scarab]

.

laws of logarithms

• is multiplication - is division

sqrt(8x) / sqrt(16x) = 1/sqrt(2)

factor out a 2 from 16