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# 7 Assorted Logarithm Problems

Please see the attached file for the fully formatted problems.

A. i) Find the natural logarithms of the values given as Items 8 and 9 on the worksheet. (Give your answer to 3d.p.
where appropriate).
ii) Refer to Item 10 on your worksheet. Using common logarithms find the value of 'x' and check your answer by numerical substitution.
iii) Find the natural anti-logs of the values given as Items 11 and 12 on the worksheet. (Give your answer to 3d.p. where
appropriate).
iv) From your worksheet, refer to the equation given as Item 13. Using common logarithms, rind the value of 'x'.

B. Refer to item 14 on your worksheet.
i) Given that 'R' is equal to Item 15 on your worksheet, find the value of 'v'.
Refer to item 16 on your worksheet.
ii) Transpose the formula to make 'ZA' the subject.
C. Refer to item 17 on your worksheet.
i) Use the laws of logarithms to prove the infornation given. At each stage explain which law of logarithms is being used.

#### Solution Preview

A) i) ln (0.16) = -1.833
ln (6.4) = 1.856

ii) 18^x-3 = 0
18^x = 3
Take log on both sides
x * log 18 = log 3
x = log 3/log 18 = 0.38
Find 18^0.38 = 3.00 Q.E.D.

iii) Natural anti-log is same as the exponential function "e"

e^4.78 = 119.104
e^0.89 = 2.435

...

#### Solution Summary

Assorted logarithm problems are solved.

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