Question

My teacher asked these questions today in class, but i got sick and wasnt able to hear the lesson and now i dont understand it please help!!!! Any help will be greatly apprecaited
A) Which of the logarithm properties may be needed when solving logarithmic equations?
B) Logarithmic equations are solved with either the one-to-one property or the definition of a logarithm . describe how to determine which method is used.
C) Is it possible for a logarithmic equation to have no solution? If so, when would this occur?
D) Is it possible for a logarithmic equation to have multiple solutions?

Answer 1

these are logarithmic properties:
\[\log_{a}b +\log_{a}c=\log_{a}(bc) \] - addtion property

Answer 2

sorry, product property

Answer 3

this is quotent property
\[\log_{a}b-\log_{a}c=\log_{a}(c/d)\]

Answer 4

this is change of base property
\[\log_{a}b=\frac{ \log_{c}b }{ \log_{c}a }\]

Answer 5

power property
\[\log_{a^p}{b^q}=\frac{ q }{ p}*\log_{a}b\]

Answer 6

the case of it is
\[\log_{a}b^p=p*\log_{a}b\]

Answer 7

another case is
\[\log_{a^p}b=1/p*\log_{a}b\]

Answer 8

these are all properties.

Answer 9

sorry for 2nd it must be b/c not c/d

Answer 10

i don't know what can be for 2nd question, but for 3rd let's look at the graph of logarithmic function.

Answer 11

this is a logarithmic function.
its equation is
\[y=\log_{a}x\]

Answer 12

where a is constant
from the graph you can see that x can't be less than 0 and be equal to 0.
Truly, let's imagine x can be negative or be 0
then a^y=x.
1) a^y=0, there are no such y that a^y=0
2) a^y=-|x|. there can't be such y so x will be negative

Answer 13

so logarithmic equation may not have a solution when the b is negative or equal to 0
\[\log_{a}b=c\]

Answer 14

for the last one there can't be multiple solutions for the equation

Answer 15

thanks