Use the following steps to prove that log b(xy)- log bx+ log by.

a. letx-bp and y= bq. solve these expressions for p and q, respectively
b. use the property b*b b to express xy in terms of b, p, and q
c. compute log b(xy) and simplify

Answer with Step-by-step explanation:

a.

Taking both sides log

Using identity:

Using identity:

b.

We know that

Using identity

c.

Substitute the values then we get

By using

Hence,

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

2425

step-by-step explanation: