Answer:x=e
Step-by-step explanation:
To solve the equation
ln
(
�
)
+
ln
(
�
2
)
=
3
ln(x)+ln(x
2
)=3, you can simplify it first by combining the logarithms:
ln
(
�
)
+
ln
(
�
2
)
=
ln
(
�
⋅
�
2
)
=
ln
(
�
3
)
ln(x)+ln(x
2
)=ln(x⋅x
2
)=ln(x
3
)
So, the equation becomes:
ln
(
�
3
)
=
3
ln(x
3
)=3
Now, to eliminate the natural logarithm, you can rewrite the equation in exponential form:
�
ln
(
�
3
)
=
�
3
e
ln(x
3
)
=e
3
�
3
=
�
3
x
3
=e
3
Now, solve for
�
x:
�
=
�
3
3
x=
3
e
3
�
=
�
x=e
