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3 years ago

For what value of x does 3^4x=27^x-3?

Mathematics

2 answers:

dalvyx [7]3 years ago

8 0

Answer:

x= - 9

Step-by-step explanation:

This problem bothers on the law of indices

Given the expression

3^4x=27^x-3

We can also simplify it using the law

3^4x= 3^3(x-3)

Equating the powers we have

4x= 3(x-3)

Opening bracket

4x= 3x-9

Collecting like terms we have

4x-3x=-9

x=-9

Indices are used to show numbers that have been multiplied by themselves. They can also be used to represent roots, such as the square root, and some fractions. The laws of indices enable expressions involving powers to be manipulated more efficiently than writing them out in full.

Setler79 [48]3 years ago

4 0

x=4.80989686

by simplifying both sides of the equation, then isolating the variable.

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4 years ago

Read 2 more answers

What is the solution of ?<img src="https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%7D%20x-7%3D%5Cfrac%7B3%7D%7B4%7D%20x%2B14" id="Tex

Nonamiya [84]

Combine the terms by multiplying into a single fraction.

$\bf{\dfrac{5}{2}x-7=\dfrac{3}{4}x+14 }$

Find the common denominator.

$\bf{\dfrac{5x}{2}-7=\dfrac{3}{4}x+14 }$

Combine fractions with the lowest common denominator.

$\bf{\dfrac{5x(-7)}{2}=\dfrac{3}{4}x+14 }$

Multiply the numbers.

$\bf{\dfrac{5x-14}{2}=\dfrac{3}{4}x+14 }$

Combine the multiplied terms into a single fraction

$\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+14 }$

Find the common denominator.

$\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+\dfrac{4\cdot14}{4} }$

Combine fractions with the lowest common denominator.

$\bf{\dfrac{5x-14}{2}=\dfrac{3x+4\cdot14}{4} }$

Multiply the numbers.

$\bf{\dfrac{5x-14}{2}=\dfrac{3x+56}{4} }$

Eliminate the denominators of the fractions.

$\bf{4\cdot\dfrac{5x-14}{2}=4\cdot\dfrac{3x+56}{4} }$

Cancel the multiplied terms that are in the denominator.

$\bf{2(5x-14)=3x+56}$

To distribute.

$\bf{10x-28=3x+56 }$

Add 28 to both sides.

$\bf{10x-28+28=3x+56+28 }$

Simplify

$\bf{10x=3x+84 }$

Subtract 3x from both sides.

$\bf{10x-3x=3x+84-3x }$

Simplify

$\bf{7x=84 }$

Divide both sides by the same factor.

$\bf{x=\dfrac{84}{7} }$

Simplify

$\bf{x=12 \ \ \ === > \ \ \ Answer}$

↓

<h3>Verification</h3>

Let x=12.

$\bf{\dfrac{5}{2}\times12-7=\dfrac{3}{4}\times12+14 }$
$\bf{\dfrac{5\times12}{2}-7=\dfrac{3}{4}\times12+14 }$
$\bf{\dfrac{60}{2}-7=\dfrac{3}{4}\times12+14 }$
$\bf{30-7=\dfrac{3}{4}\times12+14 }$
$\bf{30-7=\dfrac{3\times12}{4}+14 }$
$\bf{30-7=\dfrac{36}{4}+14 }$
$\bf{30-7=9+14 }$
$\bf{23=9+14 }$
$\bf{23=23}$

Checked ✅

3 0

2 years ago

Can u help? this is due in an hour

Marysya12 [62]

Answer:

<em> 4 pairs of earrings </em>

Step-by-step explanation:

3.75 e + 9.50 < 25

3.75 e < 25 - 9.50 = 15.50

e < 15.50 ÷ 3.75 ≈ 4.13

e =<em> 4 pairs of earrings</em>

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3 years ago

A wooden plaque is in the shape of an ellipse with height 26 centimeters and width 16 centimeters. Find an equation for the elli

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Answer:

14.19

Step-by-step explanation:

8 0

3 years ago

Consider two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible cho

yaroslaw [1]

Answer:

a) attached below

b) ( T,T )

c) The Pure-strategy Nash equilibria are : ( N,E ) and ( E,N )

d) The mixed-strategy Nash equilibrium for Firm 1 = ( 1/3 , 0, 2/3 )

while the mixed -strategy Nash equilibrium for Firm 2 = ( 1/3 , 0, 2/3 )

Step-by-step explanation:

A) write down the game in matrix form

let: E = exit at the industry immediately

T = exit at the end of the quarter

N = exit at the end of the next quarter

matrix is attached below

B) weakly dominated strategies is ( T,T )

C) Find the pure-strategy Nash equilibria

The Pure-strategy Nash equilibria are : ( N,E ) and ( E,N )

D ) Find the unique mixed-strategy Nash equilibrium

The mixed-strategy Nash equilibrium for Firm 1 = ( 1/3 , 0, 2/3 )

while the mixed -strategy Nash equilibrium for Firm 2 = ( 1/3 , 0, 2/3 ) since T is weakly dominated then the mixed strategy will be NE

Assume that P is the probability of firm 1 exiting immediately ( E )

and q is the probability of firm 1 staying till next term ( N ) ∴ q = 1 - P.

hence the expected utility of firm 2 choosing E = 0 while the expected utility of choosing N = 4p - 2q .

The expected utilities of E and N to firm 2 =

0 = 4p - 2q = 4p - 2 ( 1-p) = 6p -2 which means : p = 1/3 , q = 2/3

4 0

3 years ago