All categories

3 years ago

Solve 6^(4x+1)=5^(x-3) for x

Mathematics

2 answers:

AleksandrR [38]3 years ago

8 0

$6^{4x+1}=5^{x-3}\\\\\log6^{4x+1}=\log5^{x-3}\\\\(4x+1)\log 6=(x-3)\log 5\\\\(4x+1)\log 6-(x-3)\log 5=0\\\\4x\log 6+\log 6-x\log 5+3\log 5=0\\\\4x\log 6-x\log 5 = -3\log 5-\log 6\\\\x(4\log 6-\log 5) = -3\log 5-\log 6\\\\x=\dfrac{-3\log 5-\log 6}{4\log 6-\log 5}\\\\x=\dfrac{3\log 5+\log 6}{\log 5-4\log 6}$

myrzilka [38]3 years ago

7 0

Answer: The answer is C

Step-by-step explanation:

You might be interested in

Which function represents the exponential function f(x) = 3x after a vertical stretch by a factor of 8 and a reflection across t

irina1246 [14]

Answer:

g(x)=-8(3^x)

Step-by-step explanation:

Given: f(x)=3^x

Multiply by 8: f(x)=8(3^x)

Negate function: g(x)=-8(3^x)

5 0

2 years ago

I have to complete this in a day plz help

Bas_tet [7]

Answer:

The Sample space DOES change, each event within the sample space DOES NOT change, The probability of each event does change. The new probability of drawing a red marble is p(R)= 1/

Step-by-step explanation:

I dont know how many red marbles are in the Jar before so I cant do that for you.

5 0

3 years ago

What two formulas are necessary to find the area of a segment of a circle?

Andrew [12]

Answer:

Step-by-step explanation:

Area of a Segment in Radians A = (½) × r2 (θ – Sin θ)

Area of a Segment in Degrees A = (½) × r 2 × [(π/180) θ – sin θ]

3 0

2 years ago

Jeff has 4 red pens and 2 blue pens in his backpack. He also has 1 yellow highlighter and 4 green highlighters in his

Romashka-Z-Leto [24]

Answer:

$\frac{1}{15}$

Step-by-step explanation:

In probability,

"AND" means "multiplication"

"OR" means "ADDITION"

We want probability of Blue Pen and Yellow Highlighter. So we find individual probabilities and "MULTIPLY" them.

Let P(b) be probability of blue pen

Let P(y) be probability of yellow highlighter

We know probability of event is that event divided by total number of that

So,

There are 4 + 2 = 6 pens

Blue pen = 2

Hence,

P(b) = 2/6 = 1/3

And,

There are 5 highlighters

Yellow highlighter = 1

Hence,

P(y) = 1/5

Now,

P(b and y) = 1/3 * 1/5 = 1/15

Hence,

probability of grabbing blue pen and a yellow highlighter is $\frac{1}{15}$

3 0

2 years ago

Read 2 more answers

involving the election of officers on a committee. Assume that the committee consists of 14 members including Tasha. The same th

Yanka [14]

Answer:

There are 364 ways of filling the offices.

Step-by-step explanation:

In this case, the order of filling of the offices does not matter, so, we can figure out the different ways of filling the offices by using the combination formula:

$C^{n} _{r}=\frac{n!}{(n-r)!r!}$

where n=14 (number of members)

r=3 number of offices

n!=n·(n-1)·(n-2)·...·3·2·1

$C^{14} _{3}=\frac{14!}{(14-3)!3!}=\frac{14*13*12*11*10*9*8*7*6*5*4*3*2*1}{(11*10*9*8*7*6*5*4*3*2*1)*(3*2*1)}=\frac{14*13*12}{3*2*1} =364$

5 0

2 years ago