Question

could someone help me with 7 and 11 on this? Natural logs w/derivatives

Answer 1

where is 7 and 11?

Answer 2

sorry just posted it

Answer 3

for 7 i was able to do this:
log x^2-3x = 1 but i'm not sure what to do next

Answer 4

log (x) + log (x-3) = 1

First step is to combine the left side into ONE logarithm.

The left side is just log (x(x-3)) = 1
Now write the log equation in exponential form, you get

x(x-3) = 10
x^2 - 3x = 10
x^2 - 3x - 10 = 0
(x-5)(x+2) = 0
x = 5 and x= -2

Reject x = -2 as it doesnt check int the original equation.

x = 5 is the only solution.

Answer 5

Makes sense?

Answer 6

sorry had to reboot. but yes it does! thank you. Would u happen to be able to help me with 11 though?

Answer 7

I will start you off.........

The derivative of ln (x) is 1/x

The derivative of ln (u) = i/u du

So, the derivative of ln(lnx) is 1/ln x times 1/x = 1/xlnx

Now you want the derivative of ln(ln(lnx)))

Answer 8

you want the derivative of (1/xlnx)

Use quotient rule

Answer 9

got it thanks! I'll work it out and make sure u get it right with the answer key. really appreciate it(:

Answer 10

Welcome.