Question

I'm home schooled and having a little trouble with some of my algebra 2 if someone would be so kind to take a look at these 2 problems and maybe see if they can explain how to do them I'd appreciate it loads! thanks so much in advance! ?

" use log4 7=1.4037 and log4 3=0.7925 to approximate the value of each expression"
1) log4 21
2) log4 (7/12)

Answer 1

See below

Explanation:

`log_4 7 = x` and `log_4 3 = y`

`log_4 21 = x + y`

`log_4 frac{7}{12} = x - log_4 (3 * 4) = x - y - 1`

All I used is

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

Answer 2

1) `log_4 21 = log_4 (3cdot 7) = log_4 3 + log_4 7 approx 0.7925 + 1.4037`

2) `log_ 4 (7/12) = log_4 (7/(3 cdot 4)) = log_4 7 - log_4 3 - log_4 4 approx 1.4037 - 0.7925 - 1`

Explanation:

Kids, just say no to approximation.

OK, just this once.

Use `log_4 7=1.4037` and `log_4 3=0.7925` to approximate the value of each expression

1) `log_4 21 = log_4 (3cdot 7) = log_4 3 + log_4 7 approx 0.7925 + 1.4037`

2) `log_ 4 (7/12) = log_4 (7/(3 cdot 4)) = log_4 7 - log_4 3 - log_4 4 approx 1.4037 - 0.7925 - 1`

I leave the calculator work in your capable hands.