Question

which statements are true?
Please see picture

Answer 1

Answer:

Following are the statements:

a. logₐb - logₐc = logₐb/logₐc

False.

b. logₐB - logₐc = logₐ(b/c)

True.

c. log₄(5x+16) = log₄5x+log₄16 = 2 +log₄5x

False.

d.  log₄(5x*16) = log₄5x+log₄16 = 2 +log₄5x

True.

e. logₐ(3x)₂ = 2 logₐ3 + logₐx

False.

f. logₐ(3x)₂ = 2 logₐ3 + 2 logₐx

Answer 2

Answer:

a. False

b. True

c. False

d. True

e. False

f. True

Step-by-step explanation:

By properties of logarithms:

a. False: ㏒ₐb-㏒ₐc ≠ (㏒ₐb / ㏒ₐc) does not exists that property

b. True: (㏒ₐb)-(㏒ₐc) = ㏒ₐ(b/c)  Logarithm of a Quotient

c. False: Does not exists the property:  ㏒ₐ(c+b) = ㏒ₐc + ㏒ₐb

so

㏒₄(5x+16) ≠ ㏒₄5x + ㏒₄16 but,  ㏒₄16 + ㏒₄5x = 2 + ㏒₄5x  

because ㏒₄16 = 2.

d. True:  Logarithm of a Product: ㏒ₐ(c×b) = ㏒ₐc + ㏒ₐb

so

㏒₄(16×5x) = ㏒₄16 + ㏒₄5x = 2 + ㏒₄5x

e. False: Logarithm of a Power: ㏒ₐ(c×b)ⁿ = n ㏒ₐ(c×b) = n (㏒ₐc + ㏒ₐb) = n ㏒ₐc + n ㏒ₐb

so

㏒ₐ(3x)² ≠ 2 ㏒ₐ3 + ㏒ₐx

f. Correct use of property in point e.