Question

if log b base a =c, then log a base 1/b​ = .I want clear explanation step by step

Answer 1

Answer:

Let logb(2) = 0.3869, logb(3) = 0.6131, and logb(5) = 0.8982. Using these values, evaluate logb(10).

The trick to doing this exercise is to notice that they've asked me to find something (namely, the log of ten) which can be created out of what they've given me (namely, the logs of two and five).

Affiliate

Get homework help with Mathway!

I just need to figure out how to apply the log rules to allow for the substitutions I'm going to need to make. So:

Since 10 = 2 × 5, and since they've given me logs of 2 and 5, then it will be helpful to me to turn the 10 into the product of 2 and 5, and then use a log rule to split the log with multiplication inside into the addition of two log expressions. In other words:

logb(10) = logb(2 × 5)

= logb(2) + logb(5)

Since they gave me values for logb(2) and logb(5), I can now substitute and evaluate:

logb(2) + logb(5)

= 0.3869 + 0.8982

= 1.2851

Answer 2

Step-by-step explanation:

REFER TO THE ATTACHMENT ⚔️