All Questions
33
questions
1
vote
1
answer
87
views
Solve for $x$: $3^{2x}=5^{x-1}$
So I recently got myself an AP Precalculus book (for anyone who wants to know which book, I will have that in the "To Clarify" section at the bottom of this post) and was looking through ...
- 2,652
3
votes
2
answers
194
views
How to solve for $x$ in $2^x+4^x=8^x$
So I was bored, and decided to do some math for fun. This was mostly to see if I could still do fairly complex math. After a while, I came up with this to see if I could still do some reasonably ...
- 2,652
1
vote
2
answers
122
views
But will $(\tan(x))^{\ln(\sin(x))}$ ever equal $(\ln(\cot(x)))^{\cos(x)}$
So I was looking through the homepage of Youtube, looking for more math problems that I thought that I might be able to solve when I got bored, since either I had already solved them before, I had ...
- 2,652
-1
votes
1
answer
176
views
How to solve $b^x$=$\log_bx$?
I was looking through YouTube when I came across this video by blackpenredpen. The question was$$\text{Solve: }b^x=\log_bx$$which I thought I might be able to solve. Here is my attempt at solving it:$$...
- 2,652
2
votes
1
answer
142
views
How to solve $\ln(-2)=z$?
$$\color{white}{\require{cancel}{.}}$$So I was looking through the Youtube homepage looking for math equations that I might be able to solve and I found this video by blackpenredpen. The question was ...
- 2,652
0
votes
1
answer
96
views
Solving for y in $\log_5(3y)+\log_5(9)=\log_5(405)$
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I have been doing some fairly simple math for fun lately to see what I can remember. Other than my other question that I had about another of my ...
- 2,652
5
votes
3
answers
265
views
Solve for $x$ correct to $3$ decimal places: $27=\frac{1}{6^x}$
$\color{white}{\require{cancel}{placeholder}}$
So recently, I decided to do some fairly basic trigonometry for fun to see what I was able to remember. I decided to give myself a challenge and ...
- 2,652
3
votes
2
answers
95
views
Solve $(x^2-5x+5)^{x^2+4x-60}=1$-Missing Solution
Problem:
$$(x^2-5x+5)^{x^2+4x-60}=1$$
Attempt:
Taking logs on both sides:
$$(x^2+4x-60)\ln(x^2-5x+5)=0$$
Yields 4 solutions:
$$[1]: x^2+4x-60=(x+10)(x-6)=0 \implies x=-10,6$$
$$[2]: x^2-5x+5=1 \...
- 608
0
votes
1
answer
30
views
What is the maximum $b$ for which $\log_b(x) = \log_b(\log_b(x))$ has real solutions? And would there be 1 or 2 solutions?
$\log_b(x) = \log_b(\log_b(x))$
Based on preliminary observations on Desmos, $1.44<b<1.45$. For $b$ less than that, the identity has 2 real solutions, and for $b$ greater than that, it has 0 ...
- 467
2
votes
2
answers
648
views
What is wrong with my approach to solving $x^{\log25} + 25^{\log x} = 10\;$?
Found this equation on the web: $$x^{\log25} + 25^{\log x} = 10$$
The person solved by substitution and got $x = \sqrt{10}$ which satisfies the equation.
I tried different ways after following the man'...
- 119
0
votes
1
answer
41
views
Exponents and bases
I have some doubts in understanding the necessity of some steps in the following situation. While solving an algebraic problem, I came across an expression of the following type, where I have to solve ...
- 127
1
vote
3
answers
60
views
Proving that $f(x) = 6\ln(x^{11}-4) -2$ is one-to-one
Please verify my proof, and if there are any mistakes please explain.
Prove that that this function is one-to-one: $f(x) = 6\ln(x^{11}-4) -2$.
Suppose $f(x_1) = f(x_2)$
$\implies 6\ln(x_1^{11}-4) -2 =...
2
votes
2
answers
106
views
$\log_2(8)= a$; $\log_2(5)= b$; $\log_2(7) = c$; express $\log_2\sqrt{21}$ in terms of $a, b, c$
Not sure where to start with this question.
I could try
\begin{align}
& \frac12\log_2(21) \\[6pt]
& \frac12\log_2(7 \cdot 3) \\[6pt]
& \frac12\log_2(7) + \frac12\log_2(3) \\[6pt]
& \...
- 31
3
votes
2
answers
48
views
Is there a gap in my proof? If $a>1$ and $\log_ab_1>\log_ab_2$, then $b_1>b_2.$
I need to prove that
If $a>1$ and $\log_ab_1>\log_ab_2$, then $b_1>b_2.$
My attempts:
Let $\log_ab_1=x, \log_ab_2=y$ we have $\begin{cases} a^x=b_1 \\ a^y=b_2 \end{cases} \Longrightarrow a^...
user548054
0
votes
1
answer
36
views
Find number of solutions to the equation log
Find number of solutions to the equation $\log_{x+1}{(x-\frac{1}{2})}=\log_{x-\frac{1}{2} }{(x+1)}$
The only solutions in the complexes are 1, and 3/2?
Let $(x+1)^a=(x-\frac{1}{2})$ and thus $(x-\...
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