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# Solve the logarithmic equation $\log_{2}\left(x-2\right)+\log_{2}\left(x+1\right)=2$

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##  Final answer to the problem

$x=\frac{3+\sqrt{17}}{2},\:x=\frac{3-\sqrt{17}}{2}$
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##  Step-by-step Solution 

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• Find the derivative using the definition
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1

Express the numbers in the equation as logarithms of base $2$

$\log_{2}\left(x-2\right)+\log_{2}\left(x+1\right)=\log_{2}\left(2^{2}\right)$

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

$\log_{2}\left(x-2\right)+\log_{2}\left(x+1\right)=\log_{2}\left(2^{2}\right)$

Learn how to solve differential calculus problems step by step online. Solve the logarithmic equation log2(x+-2)+log2(x+1)=2. Express the numbers in the equation as logarithms of base 2. The sum of two logarithms of the same base is equal to the logarithm of the product of the arguments. Use the following rule for logarithms: \log_b(b^k)=k. Multiplying polynomials x-2 and x+1.

##  Final answer to the problem

$x=\frac{3+\sqrt{17}}{2},\:x=\frac{3-\sqrt{17}}{2}$

##  Explore different ways to solve this problem

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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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

###  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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