Question

calling for help (LOGS)

Answer 1

check if its right.

Answer 2

yes its right

Answer 3

the first one is right

Answer 4

the second i have no idea :/

Answer 5

Lets go over it, the first question is \[5^{2x}=10\]
\[\log_2 5^{2x} = \log_2 10 \implies x = \frac{ \log_2 10 }{ \log_2 25 }\]

Answer 6

We took the logarithm on both sides so we can bring the x down.

Answer 7

\(Log_{\text{ base }} \text{ Answer} = Exponent\)
So \( log_{2}2=1\)
So you started off correctly and landed up with the following:
\( \log _2( x+3)=4 \)
Using the property above we covert the log into an exponent
\(2^{4}=x+3\)
And then solve for x

Answer 8

wait. So letter a and b are both one problem?

Answer 9

Huh?

Answer 10

we're solving be correct?

Answer 11

No we just did a, we need to do b now.

Answer 12

I explained how to solve part B

Answer 13

okay, I see it now.

Answer 14

so now I have to solve \[_{2}4=x+3\]

Answer 15

YASSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

Answer 16

NAILED IT!

Answer 17

idk smth doesnt seem right to me

Answer 18

How did you separate \(\log_2(x+3)\)
How did you separate the x and the 3 without removing the log?

Answer 19

I first subtracted 1 from both sides Then I simplified 5-1 to 4 and got log2 (x+3)=4

Answer 20

Right you got \[ \log_2 (x+3)=4 \]
Now the Log_2 goes on the whole bracket of (x+3) you cant just divide the log_2 to get rid of it. One of the ways to get rid of it is to convert it into an exponent like i showed you above

Answer 21

soso that solution I then have to solve it?

Answer 22

Just figure out what x is?

Answer 23

scroll up and look at my solution

Answer 24

I did.

Answer 25

ok So this is basically how you can convert a log into an exponent

\[Log_{ \text{ base}} \text{ Answer } = \text{ exponent }\]

Ok here is a general example:
\[\log_a b = c \to a^c=b\]

Answer 26

So back to our example:
\[\log_2(x+3)=4 \to 2^4=x+3\]

Answer 27

And then we just solve normally
\[2^4=x+3\]
\[16=x+3\]
\[13=x\]

Answer 28

13=x

x=13

Answer 29

All the same
13 equals x
x equals 13
Both mean the same thing

Answer 30

yea .... I hope you understand it :D