Evaluating Logarithmics

• December 3rd 2008, 04:43 PM
peekaboos
Evaluating Logarithmics
Evaluate (exact answers only, show steps)

$
{\log_3}81{\sqrt{3}}
$

I got 5/2 as my answer but I'm not sure if it's right.
• December 3rd 2008, 05:40 PM
skeeter
$y = \log_3(81\sqrt{3})$

$3^y = 81\sqrt{3}$

$3^y = 3^4 \cdot 3^{\frac{1}{2}}$

$3^y = 3^{\frac{9}{2}}$

$y = \frac{9}{2}$
• December 3rd 2008, 07:22 PM
EyesForEars
You got lost when it came to adding the exponents. $a^c+a^d=a^{c+d}$
Thats not where it happened though.
When adding or subtracting fractions, you must first find a common denominator. Two fractions with different denominators cannot be added.

$
4/1+1/2
$

the lowest common mulptiple of 1 and 2 is 2

In order to make the addition or subtraction of these fractions(exponents in this case) possible. You have to first apply the fundamental property of fractions. This states that if you add, subtract, mulptiply, or divide the same thing to both top and bottom of a fraction, the resulting fraction will be equivalent to the initial fraction.

$
(2)4/(2)1 = 8/2 = 4
$

Which is equivalent to
$4/1 = 4$

So, in order to add fractions that have different denominators, you first have to find the lowest common mulptiple of the denominators. Apply the fundamental principle of fractions to make thier denominators equal to one another. Then, you can add or subtract straight accross the top, keeping the denominator on the bottom.

$
4/1+1/2
$

(Apply fundamental principle of fractions)

$
(2)4/(2)1+1/2 = 8/2+1/2
$

$
8/2+1/2 = 9/2
$