Solve the logarithmic equation $\log_{2}\left(x^2-5x-4\right)=1$

Step-by-step Solution

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Final answer to the problem

$x=-1,\:x=6$
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Step-by-step Solution

How should I solve this problem?

  • Prime Factor Decomposition
  • Solve for x
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
  • Simplify
  • Find the integral
  • Find the derivative
  • Factor
  • Factor by completing the square
  • Find the roots
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1

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

$\log_{2}\left(x^2-5x-4\right)=\log_{2}\left(2^{1}\right)$

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$\log_{2}\left(x^2-5x-4\right)=\log_{2}\left(2^{1}\right)$

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Learn how to solve problems step by step online. Solve the logarithmic equation log2(x^2+-5*x+-4)=1. Express the numbers in the equation as logarithms of base 2. Any expression to the power of 1 is equal to that same expression. 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. Group the terms of the equation by moving the terms that have the variable x to the left side, and those that do not have it to the right side.

Final answer to the problem

$x=-1,\:x=6$

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Function Plot

Plotting: $\log_{2}\left(x^2-5x-4\right)-1$

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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

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