Question

Help with logarithims

Answer 1

For the first one would you just fill in x for 0?

Answer 2

to which we would get log(10)10+3

Answer 3

yes replace x with 0

Answer 4

\[\log_a(a)=1 \text{ where } a \in (0,1) \cup (1,\infty)\]

Answer 5

since a^1 is a

Answer 6

I am confused are you saying log10(10)=1?

Answer 7

yes \[10 \in (1,\infty) \\ \text{ so } 10 \in (0,1) \cup (1,\infty) \\ \text{ so yes } \log_{10}(10)=1 \]

Answer 8

so like then we just add 3? so f(0)=4?

Answer 9

since 10^1=10

Answer 10

yep

Answer 11

and for the second one would you just divide log(10)20/log(10)3

Answer 12

yes

Answer 13

so log(3)20=x
so you just seperate? and then they both have the common log(10)? im trying to udnerstand why

Answer 14

you can solve the equation by first taking log_10 of both sides

Answer 15

\[\log_{10}(20)=\log_{10}(3^x) \\ \log_{10}(20)=x \log_{10}(3) \text{ by power rule } \]

Answer 16

then divide both sides be log_10(3)

Answer 17

Alrights Thank you for clearing that up. Egh last night of cramming for this test

Answer 18

\[\frac{\log_{10}(20)}{\log_{10}(3)}=\frac{x \log_{10}(3)}{\log_{10}(3)} \\ \frac{\log_{10}(20)}{\log_{10}(3)}=x\]

Answer 19

you could have chosen any log base
as long as that base is a number between 0 and 1 exclusive or between 1 and infinity exclusive

Answer 20

maybe they want you to express in base 5 log
well take log_5( ) of both side instead

Answer 21

just doing an example...
\[20=3^x \\ \log_5(20)=\log_5(3^x) \\ \log_5(20)=x \log_5(3) \\ \frac{\log_5(20)}{\log_5(3)}=x\]

Answer 22

notice that answer could be expressed as:
\[x=\frac{\log_a(20)}{\log_a(3)} \text{ where } a \in (0,1) \cup (1,\infty)\]

Answer 23

can we say 3^x=20?

Answer 24

yes equality is symmetrical
if a=b then b=a

Answer 25

the can we say x=log3(20)?

Answer 26

yes
my answer will also conclude that if you put a as 3
\[x=\frac{\log_3(20)}{\log_3(3)}=\frac{\log_3(20)}{1}=\log_3(20)\]

Answer 27

can't we say x as a decimal?

Answer 28

you mean approximate x ?

Answer 29

yep

Answer 30

3^1=3
3^2=9
3^3=27
so x must be between 2 and three.... and so on?

Answer 31

But if we are asked to find x for 4 decimal places can we find it? :(

Answer 32

calculator would probably be your friend

Answer 33

can we find it without using it?