1. ## Simple Log Help!

If x = log2 and y = log3, express the following in terms of x and y:

c) log15
h) log0.27
j) log0.6
l) log1.8

Thanks!

PS. All bases are 10.

2. As 15 = 30 / 2 you can express it as 10 * 3 / 2

Log 10 = 1, and you have log 3 and log 2 so use the standard combination laws: log xy = log x + log y, log (x/y) = log x / log y.

Others solved the same way - the tricksy bit here is the fact that you have powers of 10 in the mix.

$\displaystyle \log\ a + \log\ b = \log\ ab$

$\displaystyle \log\ a - \log\ b = \log\ \dfrac{a}{b}$

What can you come up with?

4. Originally Posted by eskimogenius
If x = log2 and y = log3, express the following in terms of x and y:

c) log15

$\displaystyle 15=\frac{3}{2}\cdot 10$ , and now look below.

h) log0.27

$\displaystyle 0.27=(0.3)\cdot (0.9)\Longrightarrow$ since $\displaystyle \log(a\cdot b)=\log a\cdot \log b$ , then...

j) log0.6

Just note that $\displaystyle 0.6=2\cdot (0.3)\,,\,\,0.3=\frac{3}{10}\,\,and\,\,\log(a/b)=\log a-\log b$

l) log1.8

$\displaystyle 1.8=3\cdot 0.6$ ...

Tonio

Thanks!

PS. All bases are 10.
.

5. Thanks for that. Should have thought about the questions more before I blogged them.

Sorry.

6. Originally Posted by eskimogenius
Thanks for that. Should have thought about the questions more before I blogged them.

Sorry.
You're all right. No worries. Enjoy your time here.