solve the equations ³log x = 2
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x
3log
10
3
x−
3
2
log
10
x
=10
3
7
Taking log both sides on base 10,
$$\Rightarrow\,\,\,\begin{pmatrix}3\,\log^3_{10}\,x-\displaystyle\frac{2}{3}\log_{10}\,x\end{pmatrix}\log_{10}\,x\,=\,\displaystyle\frac{7}{3}[\because \log a^m = m\log a \text& \log_aa=1]$$
Substitute log
10
x=t
⇒3t
4
−
3
2
t
2
=
3
7
⇒9t
4
−2t
2
−7=0
⇒(9t
2
+7)(t
2
−1)=0∴t=±1
⇒log
10
x=±1⇒x=10
±1
⇒x=10,
10
1
∴x
1
.x
2
=1,log
x
2
x
1
=−1,log(x
1
.x
2
)=0
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