Solve the logarithmic equation $\ln\left(y\right)=\ln\left(x^{7\sin\left(x\right)}\right)$

Step-by-step Solution

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Final answer to the problem

$y=x^{7\sin\left(x\right)}$
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Step-by-step Solution

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  • Solve for x
  • Find the derivative
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  • Solve by quadratic formula (general formula)
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For two logarithms of the same base to be equal, their arguments must be equal. In other words, if $\ln(a)=\ln(b)$ then $a$ must equal $b$

$y=x^{7\sin\left(x\right)}$

Final answer to the problem

$y=x^{7\sin\left(x\right)}$

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Function Plot

Plotting: $\ln\left(y\right)-\ln\left(x^{7\sin\left(x\right)}\right)$

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1
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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: Logarithmic Equations

Are those equations in which the unknown variable appears within a logarithm.

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