Question

Find the x value of log 2 log 6 log x are in gp

Answer 1

Answer:

the answer is 102.681

Step-by-step explanation:

log(ans)=(log6)^2/log2=2.0115

ans=10^2.0115

ans=102.68 (app.)

Answer 2

Geometric progression

The terms $a_{1}$, $a_{2}$, $a_{3}$, $a_{4}$, $a_{5}$, $...$ are in geometric progression, only when

$\quad\frac{a_{2}}{a_{1}}=\frac{a_{3}}{a_{2}}=\frac{a_{4}}{a_{3}}=...$

For three terms.

If three terms $a,\:b,\:c$ are in geometric progression, then

$\quad \frac{b}{a}=\frac{c}{b}$

$\Rightarrow b^{2}=ca$

Solution.

The given numbers $log2$, $log6$ and $logx$ are in G. P. . Then

$\quad (log6)^{2}=(log2)\:(logx)$

$\Rightarrow logx=\frac{(log6)^{2}}{log2}$

$\Rightarrow x=10^{\frac{(log6)^{2}}{log2}}$

$\Rightarrow x\approx 102.68$

Answer.

Hence the value of $x$ is $102.68$