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Ratling [72]
3 years ago
15

Which statements are true? Please see picture

Mathematics
2 answers:
azamat3 years ago
6 0

Answer:

a. False

b. True

c. False

d. True

e. False

f. True

Step-by-step explanation:

<em><u>By properties of logarithms:</u></em>

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

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

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

<em>so </em>

㏒₄(5x+16) ≠ ㏒₄5x + ㏒₄16 <em>but,</em><em>  </em>㏒₄16 + ㏒₄5x = 2 + ㏒₄5x  

<em>because</em> ㏒₄16 = 2.

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

<em>so</em>

<em> </em>㏒₄(16×5x) = ㏒₄16 + ㏒₄5x = 2 + ㏒₄5x

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

<em>so</em>

<em> </em>㏒ₐ(3x)² ≠ 2 ㏒ₐ3 + ㏒ₐx

f. Correct use of property in point e.

monitta3 years ago
5 0

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

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