Question

use the laws of loagrithms to simplify
ln(x^2y^4z^7)

Answer 1

= ln(x^2) + ln(y^4) + ln(z^7) = 2ln(x) + 4ln(y) + 7ln(z)

Answer 2

\[\log _{2}(x ^{2}\sqrt{2x-3})\]

Answer 3

= log2(x^2) + log2((2x - 3)^(1/2))

= 2log2(x) + 1/2*log2(2x - 3)

Answer 4

how did you get (1/2)?

Answer 5

the square root of m can be written as m^(1/2)

proof:

m^(1/2) * m^(1/2) = m^(1/2 + 1/2) = m^(1) = m

hence (m^(1/2))^2 = m

hence m^(1/2) = sqrt(m)

Answer 6

one last question

Answer 7

\[\log _{2}(\sqrt[3]{3x-5}/\sqrt[4]{2x+1})\]

Answer 8

= log2((3x - 5)^(1/3)) - log2((2x + 1)^(1/4))

= 1/3*log2(3x - 5) - 1/4*log2(2x + 1)

do you get it now

Answer 9

remember that the n'th root of y can be written as y^(1/n)

Answer 10

yeaa ido thanks for yur help:)

Answer 11

\[\ln{x^2y^4z^7}=\ln{x^2}+\ln{y^4}+\ln{z^7}=2\ln{|x|}+4\ln{|y|}+7\ln{z}\]\[x\neq0,y\neq0,z>0\]