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Solve the logarithmic equation $y=\frac{\log \left(\sqrt{a+bx}\right)}{\sqrt{a-bx}}$

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Solution

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Final answer to the problem

$y=\frac{\frac{1}{2}\log \left(a+bx\right)}{\sqrt{a-bx}}$
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Step-by-step Solution

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Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

$y=\frac{\frac{1}{2}\log \left(a+bx\right)}{\sqrt{a-bx}}$

Final answer to the problem

$y=\frac{\frac{1}{2}\log \left(a+bx\right)}{\sqrt{a-bx}}$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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Function Plot

Plotting: $y+\frac{-\log \left(\sqrt{a+bx}\right)}{\sqrt{a-bx}}$

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7
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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
D□x
∫
∫◻
|◻|
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:

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Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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