Conditions on the Parameters of Logarithm Function

The number of values of $x\in [0,n\pi ],n\in I$ that satisfy $lo{g}_{|sinx|}(1+cosx)=2$ is

1. None of these

2. 0

3. n

4. 2n

1. $\ge e$
2. Any positive real number $\ne 1$
3. Any positive real number
4. Any number

The number of values of $x\in [0,n\pi ],n\in I$ that satisfy $lo{g}_{|sinx|}(1+cosx)=2$ is

1. 0

2. n

3. 2n

4. None of these

1. Any positive real number $\ne 1$
2. Any number
3. Any positive real number
4. $\ge e$

For y = ${\log }_{a}x$to be defined a and x must be _____.

1. a≥ e and x > 0

2. Any positive real number for both a and x

3. Any number for both a and x

4. a is any positive real number but not equal to 1 and x > 0

1. 2
2. 1
3. 4
4. None of these

1. $\ge e$
2. Any + ive real number
3. Any number
4. any + ive real number $\ne$ 1

Solve the inequality. Graph the solution.

$-0.6>-0.3(d+6)$

1. $101$
2. $1102$
3. $1001$
4. $1101$

Solve the inequality. Graph the solution.

$-\frac{1}{4}d+1<2$

What values of $x$ make the two expressions below equal?

$\frac{\left(x+3\right)\left(x+8\right)}{5\left(x+8\right)}=\frac{x+3}{5}$

1. All real numbers.

2. All real numbers except $-3$.

3. All real numbers except $-8$.

4. All real numbers except $-8$ and $-3$.