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Solve the logarithmic equation $\log_{8}\left(x+6\right)=1-\log_{8}\left(x+4\right)$

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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 $8$

Learn how to solve simplify trigonometric expressions problems step by step online.

$\log_{8}\left(x+6\right)=\log_{8}\left(8^{1}\right)-\log_{8}\left(x+4\right)$

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Learn how to solve simplify trigonometric expressions problems step by step online. Solve the logarithmic equation log8(x+6)=1-log8(x+4). Express the numbers in the equation as logarithms of base 8. Any expression to the power of 1 is equal to that same expression. 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). 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: $\log_{8}\left(x+6\right)-1+\log_{8}\left(x+4\right)$

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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
D□x
∫
∫◻
|◻|
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:

Similar Problems Solved

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$\frac{2+tan^2x}{sec^2x}-1$

Main Topic: Simplify Trigonometric Expressions

Simplification of trigonometric expressions consists of rewriting an expression with trigonometric functions in a simpler form. To perform this task, we usually use the most common trigonometric identities, and some algebra.

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