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Andreyy89
2 years ago
13

Solve the equation e^3x-4=3​

Mathematics
2 answers:
erastova [34]2 years ago
8 0

We are given with a equation i.e ;

{:\implies \quad \sf e^{3x}-4=3}

Transpose 4 to Right-Hand-Side ;

{:\implies \quad \sf e^{3x}=7}

Now , Taking Natural logarithm to both sides ;

{:\implies \quad \sf ln(e^{3x})=ln(7)}

{:\implies \quad \sf 3x \: ln(e)=ln(7) \quad \qquad \{\because ln(a^{b})=b\: ln(a)\}}

{:\implies \quad \sf 3x=ln(7) \quad \qquad \{\because ln(e)=1\}}

{:\implies \quad \bf \therefore \quad \underline{\underline{x=\dfrac{ln(7)}{3}}}}

12345 [234]2 years ago
5 0
Answer: 0.648637

Explanation:

e^3x = 3 + 4

e^3x = 7

3x = In (7)

X = 0.648637
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Equation of Sphere =  x^{2} + y^{2} + z^{2} - 18x - 4/3y +10z + 142/3 = 0

Step-by-step explanation:

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Solving the above equation:

(x + 3))^{2} + (y - 6)^{2} + (z-3)^{2} = 4 x {(x-6)^{2} + (y-2)^{2} + (z + 3))^{2}}

x^{2} + 9 + 6x + y^{2} + 36 - 12y + z^{2} + 9 - 6z = 4 { x^{2} + 36 - 12x + y^{2} + 4 - 4y + z^{2} + 9 + 6z}

x^{2} + 9 + 6x + y^{2} + 36 - 12y + z^{2} + 9 - 6z = 4x^{2} + 144 - 48x +4y^{2} + 16 - 16y + 4z^{2} + 36 + 24z

Putting the right hand side = 0 and solving the equation:

x^{2} - 4x^{2} + y^{2} - 4y^{2} + z^{2} - 4z^{2} + 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0

-3x^{2} - 3y^{2}  -3z^{2}  + 54x + 4y -30z -142  = 0

Taking (-) common

- ( 3x^{2} + 3y^{2} + 3z^{2}  - 54x - 4y +30z + 142) = 0

3x^{2} + 3y^{2} + 3z^{2}  - 54x - 4y +30z + 142 = 0

dividing the whole equation by 3

x^{2} + y^{2} + z^{2} - 54/3x - 4/3y +30/3z + 142/3 = 0

x^{2} + y^{2} + z^{2} - 54/3x - 4/3y +30/3z + 142/3 = 0

x^{2} + y^{2} + z^{2} - 18x - 4/3y +10z + 142/3 = 0

7 0
3 years ago
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