Question

log 5-log 2x =1 help solving

Answer 1

\(\log(5)-\log(2x)=1\) like this ?

Answer 2

I guess. Its written like I wrote it.

Answer 3

there is a rule: \(\log(A)-\log(B)=\log(A\times B)\).
apply this rule to your problem

what equation do you get after applying this rule?

Answer 4

log10x?

Answer 5

my bad, the rule should say
\(\log(A)-\log(B)=\log(A\div B)\)

Answer 6

log2.5

Answer 7

\(\displaystyle \log(\frac{5}{2x})\)

Answer 8

\(\displaystyle \log(\frac{5}{2x})=1\)

Answer 9

I can't find this i my notes.

Answer 10

the rule?
well, believe me the rule does exist

Answer 11

I know the rule exist, i can't find a problem like this in my notes. so i'm having difficulty understanding

Answer 12

it's ok, we can go through it together

Answer 13

\(\displaystyle \large \log(5)-\log(2x)=1\)
this is what we had at first,

then we applied the rule: log(A)-log(B)=log(A/B)

\(\displaystyle \large \log(\frac{5}{2x})=1\)

Answer 14

so far so good?

Answer 15

yes.

Answer 16

\(\displaystyle \large \log(\frac{5}{2x})=1\)

\(\displaystyle \large \log_{10}(\frac{5}{2x})=1\)

Answer 17

ths is because unspecific base is always 10

Answer 18

ok

Answer 19

\(\displaystyle \large \log_{10}(\frac{5}{2x})=1\) -----> \(\displaystyle \large 10^1=\frac{5}{2x}\)

Answer 20

this is exponential relation with logs

Answer 21

\(\displaystyle \large 10^1=\frac{5}{2x}\)

\(\displaystyle \large 10=\frac{5}{2x}\)

Answer 22

can you solve fro x from here?

Answer 23

for* x

Answer 24

no.

Answer 25

\(\displaystyle \large 10=\frac{5}{2x}\)

\(\displaystyle \large 10\color{blue}{\times \frac{2x}{5}}=\frac{5}{2x}\color{blue}{\times \frac{2x}{5}}\)

Answer 26

multiply accordingly on both sides

Answer 27

10x/10x?

Answer 28

1/4 or 0.25?

Answer 29

\(\displaystyle \large 10\color{blue}{\times \frac{2x}{5}}=\frac{5}{2x}\color{blue}{\times \frac{2x}{5}}\)

\(\displaystyle \large 5 \times 2 \color{blue}{\times \frac{2x}{5}}=\frac{5}{2x}\color{blue}{\times \frac{2x}{5}}\)

\(\displaystyle \large \cancel{5} \times 2 \color{blue}{\times \frac{2x}{\cancel{5}}}=\frac{5}{2x}\color{blue}{\times \frac{2x}{5}}\)

\(\displaystyle \large \color{blue}{ \frac{4}{5}}x=1\)

Answer 30

\(\displaystyle \large \color{blue}{ \frac{4}{5}}x=1\)

\(\displaystyle \large x=\color{blue}{ \frac{5}{4}}\)

Answer 31

Thats not an answer?

Answer 32

X is approximately 0.91970.