How do you use the Change of Base Formula and a calculator to evaluate the logarithm #log_5 10#?

Question

Theodore Amidon · Accepted Answer

1.43

#log_ab = (log_cb)/(log_ca)# So with the logarithm #log_5 10# where a=5 and b=10 We can write it as using the change of base formula, #log_5 10 =(log_10 10)/(log_10 5) = 1/log_10 5 = 1.43#

Caleb Alexander · Answer

undefined To evaluate the logarithm log base 5 of 10 using the Change of Base Formula and a calculator, you would first apply the formula, which states that log base a of b equals log base c of b divided by log base c of a.

In this case, you can choose any base for the logarithm that your calculator supports. Common choices are base 10 (log) or base e (ln). Let's use base 10 for this example.

So, log base 5 of 10 can be rewritten as log base 10 of 10 divided by log base 10 of 5.

You would then input these values into your calculator and perform the division.

log base 10 of 10 is simply 1, as 10 raised to the power of 1 equals 10.

To find log base 10 of 5, you would input 5 into your calculator and then take the logarithm with base 10.

Once you have both values, you divide the result of log base 10 of 10 by log base 10 of 5.

The final result would be the value of log base 5 of 10.