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Is the following statement true or false? Please explain, mathematically, why or why not.
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Is the following statement true or false Please explain mathematically why or why not Please help class=


Answer :

pookerpooker29

Answer:

false

Step-by-step explanation:

Evaluate the identity

Recognize that the identity is false because the logarithm of a sum is not equal to the sum of the logarithms.

Therefore, the identity is false.

semsee45

Answer:

False

Step-by-step explanation:

Given statement:

[tex]\log_8(x-3) = \log_8 x-\log_8 3[/tex]

The statement is false because the logarithm quotient rule applies to division within the argument of the logarithm, not subtraction.

The quotient rule states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and the denominator. Therefore:

[tex]\log_8\left(\dfrac{x}{3}\right) = \log_8 x-\log_8 3[/tex]

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