Condense the logarithmic expression $\log_{2}\left(80\right)-\log_{2}\left(5\right)$

Step-by-step Solution

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Final answer to the problem

$4$
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Step-by-step Solution

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  • Condense the logarithm
  • Expand the logarithm
  • Simplify
  • Find the integral
  • Find the derivative
  • Write as single logarithm
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
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The difference of two logarithms of equal base $b$ is equal to the logarithm of the quotient: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$

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$\log_{2}\left(16\right)$

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Learn how to solve condensing logarithms problems step by step online. Condense the logarithmic expression log2(80)-log2(5). 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). Decompose 16 in it's prime factors. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Decompose 4 in it's prime factors.

Final answer to the problem

$4$

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Plotting: $4$

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1
2
3
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: Condensing Logarithms

Combining or condensing logarithms consists of rewriting a mathematical expression with several logarithms into a single logarithm, by applying the properties of logarithms.

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