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Gelneren [198K]
3 years ago
14

I NEED HELP!! please show all work

Mathematics
1 answer:
PtichkaEL [24]3 years ago
5 0

Take the logarithm of both sides. The base of the logarithm doesn't matter.

4^{5x} = 3^{x-2}

\implies \log 4^{5x} = \log 3^{x-2}

Drop the exponents:

\implies 5x \log 4 = (x-2) \log 3

Expand the right side:

\implies 5x \log 4 = x \log 3 - 2 \log 3

Move the terms containing <em>x</em> to the left side and factor out <em>x</em> :

\implies 5x \log 4 - x \log 3 = - 2 \log 3

\implies x (5 \log 4 - \log 3) = - 2 \log 3

Solve for <em>x</em> by dividing boths ides by 5 log(4) - log(3) :

\implies \boxed{x = -\dfrac{ 2 \log 3 }{ 5 \log 4 - \log 3 }}

You can stop there, or continue simplifying the solution by using properties of logarithms:

\implies x = -\dfrac{ \log 3^2 }{ \log 4^5 - \log 3 }

\implies x = -\dfrac{ \log 9 }{ \log 1024 - \log 3 }

\implies \boxed{x = -\dfrac{ \log 9 }{ \log \frac{1024}3 }}

You can condense the solution further using the change-of-base identity,

\implies \boxed{x = -\log_{\frac{1024}3}9}

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Use braces and digits to designate the set of natural numbers.
alina1380 [7]

Answer:

N = \{1,2,3,4,5,6,.....\}

Step-by-step explanation:

Required

Determine the sets of natural number

Represent this set with letter N

From definition of natural numbers, they are integer numbers starting from 1;

In other words: 1,2,3,4,5, and so on.

To represent this as a set of N, we have

N = \{1,2,3,4,5,6,.....\}

<em>The ..... means that the counting still continues</em>

6 0
3 years ago
Find the solution of the given initial value problems in explicit form. Determine the interval where the solutions are defined.
natali 33 [55]

Answer:

The solution of the given initial value problems in explicit form is y=x-x^2-2  and the solutions are defined for all real numbers.

Step-by-step explanation:

The given differential equation is

y'=1-2x

It can be written as

\frac{dy}{dx}=1-2x

Use variable separable method to solve this differential equation.

dy=(1-2x)dx

Integrate both the sides.

\int dy=\int (1-2x)dx

y=x-2(\frac{x^2}{2})+C                  [\because \int x^n=\frac{x^{n+1}}{n+1}]

y=x-x^2+C              ... (1)

It is given that y(1) = -2. Substitute x=1 and y=-2 to find the value of C.

-2=1-(1)^2+C

-2=1-1+C

-2=C

The value of C is -2. Substitute C=-2 in equation (1).

y=x-x^2-2

Therefore the solution of the given initial value problems in explicit form is y=x-x^2-2 .

The solution is quadratic function, so it is defined for all real values.

Therefore the solutions are defined for all real numbers.

4 0
3 years ago
The length of a side of a square is represented by 2x. The area of the square is
Pavlova-9 [17]
The length of a side is 18.
Here is my work attached:
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3 years ago
Solve. 45 + (-5) - 4 + 7<br> A: 45<br> B: 0<br> C: -34<br> D: 43
Helga [31]
When you add negative, it’s the same as subtracting
45 - 5 - 4 + 7
40 - 4 + 7
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The answer is D. 43
5 0
3 years ago
Read 2 more answers
What's the gradient of y=3x+1
Salsk061 [2.6K]

Answer:

3

Step-by-step explanation:

y = 3x + 1

This is in slope-y-intercept form: y = mx + c

Gradient = m = 3

4 0
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