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Solve the exponential equation $50=35+4\left(\frac{3}{4}\right)^{\frac{x}{30}}$

Step-by-step Solution

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Final answer to the problem

$x=\log_{\frac{3}{4}}\left(\frac{15}{4}\right)\cdot 30$
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Step-by-step Solution

How should I solve this problem?

  • Find the integral
  • Solve for x
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
  • Simplify
  • Find the derivative
  • Factor
  • Factor by completing the square
  • Find the roots
  • Find break even points
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Rearrange the equation

$35+4\left(\frac{3}{4}\right)^{\frac{x}{30}}=50$

Learn how to solve discriminant of quadratic equation problems step by step online.

$35+4\left(\frac{3}{4}\right)^{\frac{x}{30}}=50$

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Learn how to solve discriminant of quadratic equation problems step by step online. Solve the exponential equation 50=35+43/4^(x/30). Rearrange the equation. We need to isolate the dependent variable x, we can do that by simultaneously subtracting 35 from both sides of the equation. Canceling terms on both sides. Divide both sides of the equation by 4.

Final answer to the problem

$x=\log_{\frac{3}{4}}\left(\frac{15}{4}\right)\cdot 30$

Exact Numeric Answer

$x=-137.8351$

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Function Plot

Plotting: $50-35-4\left(\frac{3}{4}\right)^{\frac{x}{30}}$

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4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Discriminant of Quadratic Equation

Quadratic equations are those algebraic equations of the form ax^2+bx+c, where a, b, and c are constant values. The discriminant of a quadratic equation is calculated using the formula D=b^2-4ac, and it helps us to determine how many roots an equation of this type has. When D>0 the equation has two real roots, when D<0 the equation has no real roots, and when D=0 the equation has a repeated real root.

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