SOLUTION: sorry wrong equation log9 (1/3) = y (1/3 is NOT exponent) Sorry llo

Question 93393: sorry wrong equation
log9 (1/3) = y (1/3 is NOT exponent)
Sorry
llo
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
The first thing to do is to convert this logarithmic form to the exponential form using the
rule:
.
is equivalent to
.
Notice that by comparing the logarithmic form of the rule to the given problem you can
identify x as equaling y, b as equaling 9, and N as equaling . Substitute
these values into the exponential form and it becomes:
.

.
Now you can make a couple of changes. First, recognize that is equivalent to
.
Substitute this into the equation to get:
.

.
Now notice that 9 is equal to . So replace the 9 with and you get:
.

.
by the power rule of exponents you can multiply the exponent y by the exponent 2 to make the
left side of the equation change as indicated:
.

.
Notice that the bases of the two sides are both 3. Therefore, for the sides to be equal, the
two exponents must also be equal. When you set the two exponents equal you get:
.

.
Solve for y by dividing both sides by 2 to get:
.

.
That's the answer for y.
.
Check it out by substituting for y in the original problem to get ...
.

.
When you convert this to exponential form you get:
.

.
But a negative exponent becomes a positive exponent if you put it (along with its base) into
the denominator of a fraction. So becomes and the
equation is then:
.

.
Then recognize that the exponent tells you to take the square root of its base. So
means to take the square root of 9 and the square root of 9 is 3.
So you can
replace by 3 and the equation is finally reduced to:
.

.
Since this is true, you know that is the correct answer.
.
Hope this helps you to understand the problem and how it can be worked.
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