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.
