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Algebra II

Solve the equation on the interval $[0, 2 π]$
$\sin 2 x - \sin x = 0$

Baladdaa9 2022-07-25

Solve the equation.
$- 3^{2 - x} = - 81$

Lexi Mcneil 2022-07-24

As a sales person, you receive a monthly salary of $2000, plusa commission of 7% of sales. You are offered a new job at$2300 per month, plus a commission of 5% sales.
1. If you make equations for both the new job andcurernt job, what is the point of intersection? what does this poitn signify?
2. You think you can sell $20,000 worth of a product per month.

beatricalwu 2022-07-24

The numbers on the doors of four adjacent offices are consecutive odd integers. If their sum is 976 find the four office numbers.

Dean Summers 2022-07-24

Solve the given pair simultaneously. then sketch the graphs of the equations and label the intersection point
2x=3y=15
4x-9y=3

amacorrit80 2022-07-24

If an initial amount $A_{0}$ of money is invested at aninterest rate r compounded n times a year, the value of the investment after t years is:
$A = A_{0} (1 + \frac{r}{n}) ◻^{n t}$
If we let $n \to \infty$ we refer to the continuous compounding of interest. Use L'Hospital's Rule to show that if interest is compounded continuously, then the amount aftert years is
$A_{0} e^{r t}$

Awainaideannagi 2022-07-23

Logarithm Fraction Contest Math Question
The question is as follows:
If $\frac{\log_{b} a}{\log_{c} a} = \frac{19}{99}$ then $\frac{b}{c} = c^{k}$ . Compute $k$

Marcelo Mullins 2022-07-23

Derive an equation for derivative of ln x
$\frac{d}{d x} e^{x} = e^{x}$ use this fact together with the definition of the natural log $\ln x$ as the inverse of the function of $e^{x}$ to derive an equation for the derivative of $\ln x$

Alexandra Richardson 2022-07-23

Conversion of bases with logarithms
The question says if $\log_{6} (2)$ is $a$ and $\log_{5} (3)$ is $b$ , express $\log_{5} (2)$ in terms of $a$ and $b$
I have tried the change of base formula for $a b$ to no avail, can someone give me a hint to get started, and the solution, hidden behind a spoiler tag, if I get stuck? Thanks.

Luz Stokes 2022-07-23

Solve the equation for exact answer. $9^{3 x + 5} = 18$

yasusar0 2022-07-23

Solve for two variables, two equations with exponents
Solve for both k and x, where $5 = k (300)^{x}$ and $80 = k (600)^{x}$

Greyson Landry 2022-07-23

Can this log question be simplified?
$2^{l o g_{3} 5} - 5^{l o g_{3} 2} .$ I don't know any formula that can apply to it or is there a formula?? Even a hint will be helpful.

Brenton Dixon 2022-07-22

Convert a linear scale to a logarithmic scale
Given a number n, how would I convert this number into a logarithmic scale?
My logarithmic scale would range from 0 to 255 (I'm working with RGB colours), and I would expect values of n from 1 to 1,000,000.
Apologies if this is an easy question.

capellitad9 2022-07-22

If $2 \cdot l o g_{e} (x - 2 y) = l o g_{e} y + l o g_{e} x$ , then find the numerical value of $\frac{x}{y}$
My try:
$2 \cdot l o g_{e} (x - 2 y) = l o g_{e} y + l o g_{e} x$
$l o g_{e} (x - 2 y)^{2} = l o g_{e} x y$
$(x - 2 y)^{2} = x y$
But expanding the LHS doesn't give the result. What should I do further?

Livia Cardenas 2022-07-22

L'Hôpital's as x tends to infinity
I'm searching for the explanation to the limit of:
$lim_{x \to \infty} x \ln \frac{x + 1}{x - 1} .$
I know the answer is 2, but I can't seem to get there. The problem is in my textbook under a section with l'Hôpital.

Parker Bird 2022-07-22

How I could show that : $\log 1 = 0$ ?
I would be like somone to show me or give me a prove for this :
Why $\ln 1 = 0$ ?
Note that $\ln$ is logarithme népérien, the natural logarithm of a number is its logarithm to the base $e$ .
Thanks for any replies or any comments!

Alonzo Odom 2022-07-22

Solve,
$15 (p - 6) = 15 (p + 5)$

Pierre Holmes 2022-07-22

A normal human body temperature can range from ${33.2}^{\circ} C$ to ${38.2}^{\circ} C$ . This range includes variations with gender, time of day, and where the measurement is taken. Part A What is this range in $^{\circ} F$ ? Express your answer in degrees Fahrenheit. Enter your answers numerically separated by a comma.

Tamara Bryan 2022-07-22

Find general solution for the ODE
$y " - 9 y = \frac{9 x}{e^{3 x}}$

Marisol Rivers 2022-07-21

Solution for this Logarithmic Equation
Recently I was going through a problem from the book Problems in Mathematics - V Govorov & P Dybov .
$(x - 2)^{\log^{2} (x - 2) + \log (x - 2)^{5} - 12} = 10^{2} \log (x - 2)$
I tried solving by first considering $\log (x - 2)$ as a variable, say $t$ . Then I expressed $(x - 2)$ as $10^{t}$ . Then after using some properties of log, I reached till here-
$10^{t^{3} + 5 t^{2} - 12 t} = 10^{2} t$
or
$10^{t^{3} + 5 t^{2} - 12 t - 2} = t$
Now I have no idea how to approach further. The answer in the references says $x = 3, 102, 2 + 10^{- 7}$

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