Question

Log8 (t) - log8 (5) = 1

Answer 1

Answer:

t = 40

Step-by-step explanation:

Given the logarithmic expression: $log_8 (t) - log_8 5= 1$

Use the Logarithmic Property (Quotient Rule):

$log_b a - log_b c = log_b (\frac{a}{c})$

$log_8 (t) - log_8 5 = log_8 (\frac{t}{5}) = 1$

Next, using the Logarithmic Property:  $log_b b= 1$

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, $log_b b= 1$, true.  In that case, t = 40 divided by 5 results in a quotient of 8.

$log_8 (t) - log_8 5 = log_8 (\frac{t}{5}) = log_8 (\frac{40}{5}) = log_8 8 = 1$

Therefore, the value of t = 40.