Simplify the expression.
twelve to the power of log base twelve of twenty four.
a.) 24
b.) 288
c.) 3456
d.) 12

The correct answer option is A) 24.

Step-by-step explanation:

We are given the following log expression and we are to simplify it:

Here, we are going to apply the rule for solving a log problem:

So if , then it would be equal to 24.

answer:

1702.5

step-by-step explanation:

the n th term of an arithmetic progression is

= a + (n - 1)d

where a is the first term and d the common difference, hence

a + 5d = - 5 → (1) and

a + 9d = 21 → (2)

subtract (1) from (2) term by term

4d = 26 ( divide both sides by 4 )

d = = 6.5 ← common difference

substitute d = 6.5 into (1 )

a + 32.5 = - 5 ( subtract 32.5 from both sides )

a = - 37.5 ← first term

the sum to n terms of an arithmetic progression is

= [ 2a + (n - 1)d ], hence

= 15 [ - 75 + (29 × 6.5) ]

                          = 15 [ - 75 + 188.5 ]

                          = 15 × 113.5

                          = 1702.5