a)

b)

c)

d)

e)

f)

Zoe Oneal
2021-11-06
Answered

Given that ${\mathrm{log}}_{a}\left(5\right)\approx 0.65$ and ${\mathrm{log}}_{a}\left(3\right)\approx 0.44$ , evaluate each of the following. Hint: use the properties of logarithms to rewrite the given logarithm in terms of the logarithms of 5 and 3

a)${\mathrm{log}}_{a}\left(0.6\right)$

b)${\mathrm{log}}_{a}\left(\sqrt{3}\right)$

c)${\mathrm{log}}_{a}\left(15\right)$

d)${\mathrm{log}}_{a}\left(25\right)$

e)${\mathrm{log}}_{a}\left(75\right)$

f)${\mathrm{log}}_{a}\left(1.8\right)$

a)

b)

c)

d)

e)

f)

You can still ask an expert for help

jlo2niT

Answered 2021-11-07
Author has **96** answers

Step1

${\mathrm{log}}_{a}\left(5\right)\approx 0.65{\mathrm{log}}_{a}\left(3\right)\approx 0.44$

properties of logarithms are

1.$\mathrm{log}\left(ab\right)={\mathrm{log}}_{c}\left(a\right)+{\mathrm{log}}_{c}\left(b\right)$

2.${\mathrm{log}}_{c}\left(\frac{a}{b}\right)={\mathrm{log}}_{c}\left(a\right)-{\mathrm{log}}_{c}\left(b\right)$

3.${\mathrm{log}}_{c}\left({a}^{b}\right)=b{\mathrm{log}}_{c}a$

Step2

${\mathrm{log}}_{a}\left(0.6\right)={\mathrm{log}}_{a}\left(\frac{3}{5}\right)$

${\mathrm{log}}_{a}\left(0.6\right)={\mathrm{log}}_{a}\left(3\right)-{\mathrm{log}}_{a}\left(5\right)$

${\mathrm{log}}_{a}\left(0.6\right)=0.44-0.65$

${\mathrm{log}}_{a}\left(0.6\right)=-0.21$

Step3

${\mathrm{log}}_{a}\left(\sqrt{3}\right)={\mathrm{log}}_{a}\left({3}^{\frac{1}{2}}\right)$

${\mathrm{log}}_{a}\left(\sqrt{3}\right)=\frac{1}{2}{\mathrm{log}}_{a}\left(3\right)$

${\mathrm{log}}_{a}\left(\sqrt{3}\right)=\frac{1}{2}\cdot 0.44$

${\mathrm{log}}_{a}\left(\sqrt{3}\right)=0.22$

Step4

${\mathrm{log}}_{a}\left(15\right)={\mathrm{log}}_{a}(5\cdot 3)$

${\mathrm{log}}_{a}\left(15\right)={\mathrm{log}}_{a}\left(5\right)+{\mathrm{log}}_{a}\left(3\right)$

${\mathrm{log}}_{a}\left(15\right)=0.65+0.44$

${\mathrm{log}}_{a}\left(15\right)=1.09$

Step5

${\mathrm{log}}_{a}\left(25\right)={\mathrm{log}}_{a}\left({5}^{2}\right)$

${\mathrm{log}}_{a}\left(25\right)=2{\mathrm{log}}_{a}\left(5\right)$

${\mathrm{log}}_{a}\left(25\right)=2\cdot 0.65$

${\mathrm{log}}_{a}\left(25\right)=1.3$

Step6

${\mathrm{log}}_{a}\left(75\right)={\mathrm{log}}_{a}(25\cdot 3)$

properties of logarithms are

1.

2.

3.

Step2

Step3

Step4

Step5

Step6

asked 2021-02-11

The stature of men is normally distributed, with a mean of 69.0 inches and a standard deviation of 2.8 inches. The height of women is normally distributed, with a mean of 63.6 inches and a standard deviation of 2.5 inches. Modeling academy standards require women to be models taller than 66 inches (or 5 feet 6 inches). What percentage of women meet this requirement?

asked 2020-12-29

a) Use base b = 10, precision k = 4, idealized, chopping floating-point arithmetic to show that fl(g(1.015)) is inaccurate, where

asked 2020-11-09

Use the appropriate Lagrange interpolating polynomials to find the cubic polynomial whose graph passes through the given points. $(1,2),(2,1),(3,3),(6,1)(1,2),(2,1),(3,3),(6,1)$ .

asked 2022-05-09

Compute $$(-1914)\xf733$$.

asked 2022-05-07

Compute $$(-903)\xf7(-21)$$.

asked 2021-11-19

Solve the equation.

$x+\sqrt{5x+19}=-1$

asked 2021-03-06

Show the following simultaneous equations in matrix form: