Question

PLEASE HELP!!! THX

Answer 1

Answer:  1) Product property of logarithm,

2) Subtraction property of logarithm

3) Equality property of logarithm

Step-by-step explanation:

By the Product property of logarithm,

log a + log b = log(a.b)

And, By the Subtraction property of logarithm

log a - log b = log(a/b)

Also, by the equality property of logarithm,

log(a) = log(b) ⇒ a = b

Given expression,

$log_2(5)+log_2(x+2)-log_2(x+1)=log_2(7)$                                                                

$\implies log_2(5(x+2))-log_2(x+1))=log_2(7)$  (Product property of logarithm)

$\implies log_2(\frac{5(x+2)}{2(x+1)})=log_2(7)$  (Subtraction property of logarithm)

$\implies \frac{5(x+2)}{2(x+1)}=7$   ( Equality property of logarithm )

$\implies 5(x+2)=7(x+1)$    ( Multiplicative property of equality )

$\implies 5x+10=7x+7$  ( Distributive property of equality )

$\implies 3=2x$    (subtraction property of equality )

$x=\frac{3}{2}$       (division property of equality )

Answer 2

Answer:

Product property of Log

Quotient property of Log

Equality property of log

(I just did it. It showed me that this was the correct answer. Good luck any future person reading this.)