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log8 (t) - log8 (5) = 1

Sagot :

djtwinx017

Answer:

t = 40

Step-by-step explanation:

Given the logarithmic expression: [tex]log_8 (t) - log_8 5= 1[/tex]

Use the Logarithmic Property (Quotient Rule):

[tex]log_b a - log_b c = log_b (\frac{a}{c})[/tex]

[tex]log_8 (t) - log_8 5 = log_8 (\frac{t}{5}) = 1[/tex]

Next, using the Logarithmic Property:  [tex]log_b b= 1[/tex]

We must determine the possible value of t that can be divided by 5 to produce a quotient of 8 that will make the logarithmic property, [tex]log_b b= 1[/tex], true.  In that case, t = 40 divided by 5 results in a quotient of 8.

[tex]log_8 (t) - log_8 5 = log_8 (\frac{t}{5}) = log_8 (\frac{40}{5}) = log_8 8 = 1[/tex]

Therefore, the value of t = 40.

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