Solve the logarithmic equation $\log_{6}\left(x+8\right)+\log_{6}\left(x+3\right)=1$

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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1

Express the numbers in the equation as logarithms of base $6$

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$\log_{6}\left(x+8\right)+\log_{6}\left(x+3\right)=\log_{6}\left(6^{1}\right)$

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Learn how to solve problems step by step online. Solve the logarithmic equation log6(x+8)+log6(x+3)=1. Express the numbers in the equation as logarithms of base 6. Any expression to the power of 1 is equal to that same expression. The sum of two logarithms of the same base is equal to the logarithm of the product of the arguments. 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.

Final answer to the problem

$x=-2$

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Function Plot

Plotting: $\log_{6}\left(x+8\right)+\log_{6}\left(x+3\right)-1$

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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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