Question

Help
Use the following function.
log4(x + 3) = 2
The second step would be:
Select one:
a. Take the square root of each side.
b. Take the log of each side.
c. Divide each side by 16.
d. To simplify the equation using inverses to isolate for x.

Answer 1

you might want to clarify if your equation is

\[\log4(x+3)=2\]or \[\log_{4}(x+3)=2\]

Answer 2

the 2nd one sorry

Answer 3

hint:
using the definition of logarithm, we can write:
\[\huge 2 = {\log _4}16\]

Answer 4

ok... so if you raise each term as a power of the base then you will be able to solve it

if

\[\log_{a}(b) = n\]

then

\[a^{\log_{a}(b)} = a^n\]

which can be simplified to

\[b = a^n\]

you need to apply this rule for logs to your porblem

where a = 4, b = x + 3 and n = 2

hope it helps

Answer 5

okay so once we write that @Michele_Laino what do we do next?

Answer 6

using my identity above, we can rewrite your equaton as follows:
\[\huge {\log _4}\left( {x + 3} \right) = {\log _4}16\]

Answer 7

then we can equate the numbers of both logarithm, like below:
\[\huge x + 3 = 16\]
please solve for \(x\)

Answer 8

13

Answer 9

i still dont understand for the answer .. what was the 2nd step?

Answer 10

that's right!
So, what is the right option?

Answer 11

B?

Answer 12

as we can see, when I wrote my identity, I took the logarithm of both sides, so you are right, it is option B

Answer 13

thanks can you help me again?

Answer 14

ok!

Answer 15

Use the following equation:
log2x + log2(x – 7) = 3
The second step would be to:
Select one:
a. Divide both sides by 3 to simplify.
b. Re-write the equation using the definition of logarithms.
c. Add (x – 7) to both sides to simplify.
d. Either A or C

Answer 16

If I use the definition of logarithm, I can write this:
\[\huge 3 = {\log _2}8\]

Answer 17

oh okay

Answer 18

so the 2nd step would be Re-write the equation using the definition of logarithms.

Answer 19

after that it is simple to solve the logarithm equation. So what is the right option?

Answer 20

that's right! It is option B

Answer 21

Hey i need help in another one i think i got the answer to it but i need to make sure ill tag you in it ??

Answer 22

ok!

Answer 23

hold on!