Step-by-step Solution

Solve the logarithmic equation $2\log \left(x\right)-\log \left(x+6\right)=0$

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
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Step-by-step solution

Problem to solve:

$2log\left(x\right)-log\left(x+6\right)=0$

Learn how to solve logarithmic equations problems step by step online.

$\log \left(x^2\right)-\log \left(x+6\right)=0$

Unlock this full step-by-step solution!

Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation 2log(10,x)-log(10,x+6)=0. Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right), where a=2 and b=10. 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). Rewrite the number 0 as a logarithm of base 10. 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

$x=3$
$2log\left(x\right)-log\left(x+6\right)=0$

Main topic:

Logarithmic Equations

Related Formulas:

1. See formulas

Time to solve it:

~ 0.08 s