SOLUTION: Can you please help me use log_5 2 is similar to 0.4307 and log_5 3 is similar to 0.6826 to approximate the value of log_5 10/3? (5 being the base in all instances)

Question 189536This question is from textbook algebra 2
: Can you please help me use log_5 2 is similar to 0.4307 and log_5 3 is similar to 0.6826 to approximate the value of log_5 10/3? (5 being the base in all instances) This question is from textbook algebra 2

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Can you please help me use log_5 2 is similar to 0.4307 and log_5 3 is similar to 0.6826 to approximate the value of log_5 10/3? (5 being the base in all instances)
.
Because we can rewrite (using log rules)
log_5 10/3
as
log_5 10 - log_5 3
log_5 (2*5) - log_5 3
(log_5 2 + log_5 5) - log_5 3
.
We can now use the given values of:
log_5 2 is similar to 0.4307 and log_5 3 is similar to 0.6826
Additionally, we know that
log_5 5 = 1 (because 5^1 is 5)
.
(log_5 2 + log_5 5) - log_5 3
Substituting in our values we have:
(0.4307 + 1) - 0.6826
1.4307 - 0.6826
0.7481

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