Solve the logarithmic equation $2\log \left(3x\right)=\log \left(x\right)+1$

Step-by-step Solution

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Final answer to the problem

$x=\frac{10}{9}$
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Step-by-step Solution

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Apply the formula: $a\log_{b}\left(x\right)$$=\log_{b}\left(x^a\right)$

$\log \left(\left(3x\right)^2\right)=\log \left(x\right)+1$

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

$\log \left(\left(3x\right)^2\right)=\log \left(x\right)+1$

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Unlock the first 3 steps of this solution

Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation 2log(3*x)=log(x)+1. Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right). Express the numbers in the equation as logarithms of base 10. 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.

Final answer to the problem

$x=\frac{10}{9}$

Exact Numeric Answer

$x=1.1111111$

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Function Plot

Plotting: $2\log \left(3x\right)-\log \left(x\right)-1$

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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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