Question

Evalute log 2(x-2) + log 2 (x+5)=3

Answer 1

@Zarkon

Answer 2

familiar with the log properties ?

Answer 3

yes

Answer 4

okay so apply one of them at left side \[\huge\rm \log_2(x-2) \color{reD}{+} \log_2 (x+5)=3\]
there is plus sign
whichnoe one would you use ?
quotient or product property ?

Answer 5

product

Answer 6

yes \[\huge\rm log_b x + \log_b y = \log_b(x \times y)\]
try to apply this on ur original question
pretty sure you can do it!

Answer 7

x^2+3x-10

Answer 8

yes \[\huge\rm log_2 (x^2+3x-10)=3\]
now we have to convert log to exponential form

Answer 9

x^2+3x=13

Answer 10

how did you get 13 ?

Answer 11

ohh well log_2 is still there
\[\huge\rm log_b x + \log_b y = \color{ReD}{\log_b}(x \times y)\]
\[\huge\rm\color{reD}{ log_2} (x^2+3x-10)=3\]
log_b is a common factor

Answer 12

now what do i do?

Answer 13

now, exponentiate both sides of the equation, with the base 2

Answer 14

What does that mean?

Answer 15

convert log to exponential form