3. Condense the expression into the log of a single quantity:(3logx+2logy-logz) 6. Find the number of.years required for a $2000 investment to triple at a9% interest rate compounded continuously. Give answer to nearest year.6,000A=Pert2 000Ans. ,

Answered: 6. Find the nimber of.years required…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 51RE

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Question

3. Condense the expression into the log of a single quantity:
(3logx+2logy-logz)

6. Find the number of.years required for a $2000 investment to triple at a
9% interest rate compounded continuously. Give answer to nearest year.
6,000
A=Pert
2 000
Ans. ,

Expert Solution

Concept used

The formula for continuous compounding is $A = p e^{r t}$

where $A$ is the final amount

$p$ is principal amount

$r$ is annual rate of interest in decimal form

$t$ is time in years.

Solution for the given Problem

$\frac{1}{5} [3 \log (x) + 2 \log (y) - \log (z)] = \frac{1}{5} [\log x^{3} + \log y^{2} - \log z] [as nlog (a) = \log {(a)}^{n}] = \frac{1}{5} [\log (x^{3} y^{2}) - \log z] [as \log (a) + \log (b) = \log (a b)] = \frac{1}{5} [\log \frac{x^{3} y^{2}}{z}] [as \log (a) - \log (b) = \log (\frac{a}{b})] = \log {(\frac{x^{3} y^{2}}{z})}^{\frac{1}{5}} [as n \log (a) = \log {(a)}^{n}]$

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