Question

1. For which value of x is the expression log base 4 of (x+3) not defined?

a. 0
b. -2
c. 3
d. -4

2. If log 7= a, what is the value of log 490 in terms of a?

3. For what value of k will the graph of y=log base 7 of x contain the point (1,k)?

Answer 1

1.

`log_a b \\ a>0 \hbox{ and } a \\ot=1 \\ b>0 \\ \\ log_4 (x+3) \\ x+3>0 \\ x>-3`

log₄(x+3) is defined for x greater than -3.
0>-3
-2>-3
3>-3
4≤-3
The answer is D. -4.

2.

`\log 7=a \\ \\ \log 490= \log (7^2 \cdot 10)=\log 7^2 + \log10=2 \log 7 + 1=2a+1`

The formulas I used:

`\log_a (x \cdot y)=\log_a x + \log_a y \\ \log_a x^y=y \log_a x \\ \log x=\log_(10) x`

3.

`y=\log_7 x \\ \\ (1,k) \\ x=1 \\ y=k \\ \\ k=\log_7 1 \\ k=\log_7 7^0 \\ k=0`