Use common logarithms or natural logarithms and a calculator to evaluate to four

Maiclubk

Maiclubk

Answered question

2021-10-28

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places : log1657.2

Answer & Explanation

Tasneem Almond

Tasneem Almond

Skilled2021-10-29Added 91 answers

Step 1 
Given: 
log1657.2 
To find: 
Logarithms or natural logarithms and a calculator to evaluate to four decimal places 
Step 2 
For the above logarithmic function, with the base b=16 given by, log1657.2     (1) 
Using the change of base property, 
To write a logarithm with the base b=16 in terms of common logarithm with base "10" 
That can be evaluated with a calculator. 
Thus, 
Using common logarithm to evaluate logbM as follows, logbM as follows, 
logbM=logMlogb 
log1657.2=log57.2log16      (2) 
Where we can evaluate the approximation value of the following common log function given in equation (2), 
Using the scientific and graphing calculator, respectively as follows, 
scientific calculator: 
57.2LOG÷16LOG= 
And 
Graphing calculator: 
57.2 LOG  ÷  16 LOG= 
LOG 57.2  ÷  LOG 16 ENTER 
This should approximately by, 
log16(57.2)=log(57.2)log(16)=1.75741.20412=1.459491.4595 
This means that, 
log16(57.2)1.4595 
Which is required.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?