Solve the logarithmic equation $\log_{4}\left(7\right)-\log_{4}\left(3x+4\right)=\log_{4}\left(21\right)$

Step-by-step Solution

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Final answer to the problem

$x=-\frac{11}{9}$
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Step-by-step Solution

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The difference of two logarithms of equal base $b$ is equal to the logarithm of the quotient: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$

$\log_{4}\left(\frac{7}{3x+4}\right)=\log_{4}\left(21\right)$

Learn how to solve logarithmic equations problems step by step online.

$\log_{4}\left(\frac{7}{3x+4}\right)=\log_{4}\left(21\right)$

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Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation log4(7)-log4(3*x+4)=log4(21). The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right). For two logarithms of the same base to be equal, their arguments must be equal. In other words, if \log(a)=\log(b) then a must equal b. Take the reciprocal of both sides of the equation. Apply fraction cross-multiplication.

Final answer to the problem

$x=-\frac{11}{9}$

Exact Numeric Answer

$x=-1.2222222$

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Function Plot

Plotting: $\log_{4}\left(7\right)-\log_{4}\left(3x+4\right)-\log_{4}\left(21\right)$

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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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