Natural logs (ln ) questions.......

1. Write as a single term...........5lna - 3lnb - 4= I dont get what to do with the four..?
2. If log 2 =x and log 7=y, write an expression for log 1400 in terms of x and y.

THANKS guys!! I really appreciate it:) yes ill choose a best answer soon:)

you need to remember a few rules.

one is:

rule 1: log a + log b = log (a*b)

rule 2: log a - log b = log (a/b)

rule 3: c * log a = log (a^c).

so:

5 ln a - 3 ln b - 4

-->

5 ln a = ln (a^5). by rule 3

3 ln b = ln (b^3) by rule 3

ln(a^5) - ln (b^3) = ln (a^5 / b^3)

so the answer is ln (a^5 / b^3) - 4.

we can write log 1400 = log (2 * 7 * 100) .

by rule 1:

log 1400 = log 2 + log 7 + log 100

log 2 = x , log 7 =y and log 100 = 2 (since 10^2 = 100)

so log 1400 = x + y + 2.

move the 4 over. 5lna-3lnb = 4.
combine the logs. ln((a^5)/(b^3)) = 4

1. ln[a^5 /(b^3 * e^4)]

2. log 1400 = log 2*7*100 = log 2 + log 7 + log 100 = x + y + 2

Q1)
5lna-3lnb- 4*(1)
= ln a^5 -ln b^3 -4 ln e
= ln(a^5/b^3) -ln e^4
=ln[a^5/(b^3 e^4)]


Q2

4X+Y+ 3*log 5