Solve the logarithmic equation $\log_{2}\left(5x-8\right)=\log_{2}\left(6-x^2\right)$

Step-by-step Solution

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Final answer to the problem

$x=2$
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Step-by-step Solution

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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 $b$

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$5x-8=6-x^2$

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Learn how to solve problems step by step online. Solve the logarithmic equation log2(5*x+-8)=log2(6+-1*x^2). 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. Add the values 6 and 8. Move everything to the left hand side of the equation.

Final answer to the problem

$x=2$

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Function Plot

Plotting: $\log_{2}\left(5x-8\right)-\log_{2}\left(6-x^2\right)$

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Go!
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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