Logs!! HELP!

1) Given that p = logq (16), express in terms of p:
a)logq (8q)

2)a)Given that log3 (x) = 2, determine the value of x
b) calculate the value of y for which 2log3 (y) - log3 (y+4) = 2
c) calculate the values of z for which log3 (z) = 4logz (3)

3)solve. giving ur answer as exact fractions, the simultaneous equations:
8^y = 4^(2x+3)
log2 (y) = log2 (x) +4

Please state any equations you've used... I really don't understand longs. Please be very clear.

I don't know how to do subscript here, so log2 (x) means log to the base 2

Reply 1

habosh

W@t3R

1) Given that p = logq (16), express in terms of p:
a)logq (8q)
logq8+logqq
3p/4 +1
2)a)Given that log3 (x) = 2, determine the value of x
3^2=9
b) calculate the value of y for which 2log3 (y) - log3 (y+4) = 2
log3(y^2/y+4)=(log3)9
y^2-9-36=0
y=12 ignore other solutions

c) calculate the values of z for which log3 (z) = 4logz (3)
use (lnz/ln3)=(ln81/lnz)
you get z=9
3)solve. giving ur answer as exact fractions, the simultaneous equations:
8^y = 4^(2x+3)
log2 (y) = log2 (x) +4
yln8=(2x+3)ln 4 ...continue from here

Please state any equations you've used... I really don't understand longs. Please be very clear.

I don't know how to do subscript here, so log2 (x) means log to the base 2

answers are added under questions

Reply 2

W@t3R

Why:
1) Given that p = logq (16), express in terms of p:
a)logq (8q)
logq8+logqq
3p/4 +1

Why is logq(8) = 3p/4?

Also for this one:
c) calculate the values of z for which log3 (z) = 4logz (3)
use (lnz/ln3)=(ln81/lnz)
you get z=9

It says that the answer is 1/9, 9

Reply 3

Fermat

W@t3R

Why:
1) Given that p = logq (16), express in terms of p:
a)logq (8q)
logq8+logqq
3p/4 +1

Why is logq(8) = 3p/4?
...

You have,
logq (16) = p
logq (2^4) = p
4logq (2) = p
logq (2) = p/4
===========

now,
logq(8) = logq (2^3)
logq (8) = 3logq (2)
logq (8) = (3/4)p - using logq (2) = p/4
=============

W@t3R

...

Also for this one:
c) calculate the values of z for which log3 (z) = 4logz (3)
use (lnz/ln3)=(ln81/lnz)
you get z=9

It says that the answer is 1/9, 9

You have,
(lnz/ln3)=(ln81/lnz)
(lnz)² = ln3*ln81 = ln3*ln(3^4)
(lnz)² = ln3*4ln3
(lnz)² = 4*(ln3)²
lnz = ± 2ln3
lnz = ± ln9
lnz = ln9 or lnz = -ln9 = ln9^(-1) = ln(1/9)
z = 9, or z = 1/9
=============

Reply 4

W@t3R

habosh

b) calculate the value of y for which 2log3 (y) - log3 (y+4) = 2
log3(y^2/y+4)=(log3)9
y^2-9-36=0
y=12 ignore other solutions

Why do u ignore the other solutions?

Reply 5

habosh

W@t3R

Why do u ignore the other solutions?

because it';s negative

Reply 6

Fermat

There are only two solutions, y = 12 and y = -3.

The solution y = 12 can satisfy the eqn given, i.e. 2log3 (y) - log3 (y+4) = 2
But the solution y = -3 means that you will be trying to get the log of a negative number in the 2log3 (y) bit. So that solution is to be ignored.

If you rearrange the eqn to give,

ln3 y²- log3 (y+4) = 2

then you can use the y=-3 solution since the y is squared first ( making it +ve) before a log is taken of it.