DB125: Maths for Diploma Studies: Logarithms Reinforcement Questions

Logarithms Reinforcement Questions

What is the log₁₀ of 285?

Logarithms are the exponents we need to apply to the base to get the product. So here we are looking for the exponent of 10 required to make 285. So if we call the number we are looking for $begin mathsize 14px style x end style$ :

$begin mathsize 14px style 10 to the power of x space equals space 285 end style$

This is a job for a calculator. We just need to enter 285 and then press the log button, and it gives us 2.46. So:

$begin mathsize 14px style 285 space equals space 10 to the power of 2.46 end exponent end style$

pH is the negative log₁₀ of H⁺ions. What is the concentration of H⁺ ions in a product with a pH of 3.85?

In this case, we are looking for the product of the raising 10 by the power of -3.85, so we can use the $begin mathsize 14px style 10 to the power of x end style$ button. So we have:

$begin mathsize 14px style 10 to the power of negative 3.85 end exponent space equals space 1.41 space cross times space 10 to the power of negative 4 end exponent space m o l e s space o f space H to the power of plus space i o n s end style$

If 3 is the exponent and 18 is the logarithm, what is the base?

If we call the base we are looking for $x$ :

$begin mathsize 14px style x cubed space equals space 18 end style$

If $begin mathsize 14px style x cubed end style$ is 18, the cube root of 18 must be $begin mathsize 14px style x end style$ so our base is:

$begin mathsize 14px style x space equals space cube root of 18 space equals space 2.62 end style$

And so:

$begin mathsize 14px style l o g subscript 2.62 end subscript space left parenthesis 18 right parenthesis space equals space 3 end style$

A solution as an H⁺ concentration has of 1.2 × 10^-11 M. What is the pH?

pH is the antilog of the concentration, so we can use your calculator to calculate the –Log10 of 1.2 × 10^-11:

$begin mathsize 14px style negative l o g subscript 10 space left parenthesis 1.2 cross times 10 to the power of negative 11 end exponent right parenthesis space equals space 10.92 end style$

What is 25 × ln(18)?

This one is a simple calculation:

$begin mathsize 14px style l n left parenthesis 18 right parenthesis space equals space 2.89 end style$

So:

$begin mathsize 14px style 25 space cross times space 2.89 space equals space 72.26 end style$

Next, we are going back to our roots!

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Maths for Diploma Studies

Logarithms Reinforcement Questions

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