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Solve the logarithmic equation $\log_{3}\left(56\right)-\log_{3}\left(n\right)=\log_{3}\left(7\right)$

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Solution

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Final answer to the problem

$n=8$
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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: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$

Learn how to solve integral calculus problems step by step online.

$\log_{3}\left(\frac{56}{n}\right)=\log_{3}\left(7\right)$

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Learn how to solve integral calculus problems step by step online. Solve the logarithmic equation log3(56)-log3(n)=log3(7). 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

$n=8$

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Function Plot

Plotting: $\log_{3}\left(56\right)-\log_{3}\left(n\right)-\log_{3}\left(7\right)$

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a
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n
u
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x
y
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.
(◻)
+
-
×
◻/◻
/
÷
◻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

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Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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