Question

Pre-calculus 12 Question!
Logarithm function convert to exponential function!

Convert this to exponential form:

y= 2 log3 (2x)

Answer 1

you gottta bring in the two first

Answer 2

i.e. start with \[y=\log_3(4x^2)\]

Answer 3

this is what I think: 3^y/2 = 2x

Answer 4

then \[y=\log_b(x)\iff b^y=x\]

Answer 5

oh I did not know you can times the 2 out side with inside 2x?

Answer 6

you could write it your way, yes

Answer 7

\[y=2\log_3(2x)\\
\frac{y}{2}=\log_3(2x)\\
3^{\frac{y}{2}}=2x\]

Answer 8

I see

Answer 9

which is the same as \[3^y=(2x)^2\\
3^y=4x^2\]

Answer 10

yes

Answer 11

i used this first \[n\log_b(x)=\log_b(x^n)\]

Answer 12

get the same answer of course

Answer 13

just a quick check:

I looked up on desmos,

y= log3 (4x) does not equal y = 2 log 3 (2x)

Answer 14

@satellite73

Answer 15

no it doesn't

Answer 16

\[2\log(2x)=\log((2x)^2)=\log(4x^2)\]

Answer 17

including base 3?

Answer 18

including base your favourite number
base is irrelevant, it is a property of any log

Answer 19

ok got it. Thank you :)

Answer 20

yw