Solve the logarithmic equation $\log_{8}\left(9\right)-\log_{8}\left(x+2\right)=1$

Step-by-step Solution

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Final answer to the problem

$x=-\frac{7}{8}$
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Step-by-step Solution

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1

The difference of two logarithms of equal base $b$ is equal to the logarithm of the quotient: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$

$\log_{8}\left(\frac{9}{x+2}\right)=1$

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$\log_{8}\left(\frac{9}{x+2}\right)=1$

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Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation log8(9)-log8(x+2)=1. 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). Take the variable outside of the logarithm. Any expression to the power of 1 is equal to that same expression. Simplifying the logarithm.

Final answer to the problem

$x=-\frac{7}{8}$

Exact Numeric Answer

$x=-0.875$

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Function Plot

Plotting: $\log_{8}\left(9\right)-\log_{8}\left(x+2\right)-1$

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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

How to improve your answer:

Main Topic: Logarithmic Equations

Are those equations in which the unknown variable appears within a logarithm.

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