# Which logarithm property is this?

• Mar 2nd 2013, 06:57 PM
zsf1990
Which logarithm property is this?
In this equation:
http://c811129.r29.cf2.rackcdn.com/se03c01023.png

Which logarithm property is used to change log base 4 to log base 2? Is it just an application of the change of base theorem? Everything else makes sense to me but that.

EDIT: I feel dumb now. I just realized that it's the change of base theorem being used to change the base to log base 2, thus giving a simplified answer.
• Mar 2nd 2013, 10:05 PM
Soroban
Re: Which logarithm property is this?
Hello, zsf1990!

Here is another approach.

Quote:

$\text{23. Evaluate: }\,\log_48$

$\text{Let }\,\log_48 \,=\,x$

$\text{Then: }\,4^x \:=\:8$

$\text{Get the same base on both sides:}$

. . $(2^2)^x \:=\:2^3 \quad\Rightarrow\quad 2^{2x} \:=\:2^3$

$\text{Equate exponents:}$
. . $2x \:=\:3 \quad\Rightarrow\quad x \:=\:\frac{3}{2}$