If $log_ba=1/x and log_a √b =3x^2$ , show that x =1/6?

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If $log_ba=1/x and log_a √b =3x^2$ , show that x =1/6?

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Answer 1 · 2018-06-03T18:21:08

$"see explanation"$

Explanation:

$"using the "color(blue)"law of logarithms"$

$•color(white)(x)log_b x=nhArrx=b^n$

$log_b a=1/xrArra=b^(1/x)$

$log_a b^(1/2)=3x^2rArrb^(1/2)=a^(3x^2)$

$"substitute "a=b^(1/x)" into "a^(3x^2)$

$b^(1/2)=(b^(1/x))^(3x^2)=b^(3x)$

$"we have "b^(1/2)=b^(3x)$

$3x=1/2$

$"divide both sides by 3"$

$x=(1/2)/3=1/6$

Answer 2 · 2018-06-03T18:21:31

$x=1/6$

Explanation:

$log_b a=1/x$

So

$xlog_ba=1$

$x=1/log_b a$

$x=log_ab$

Now

$1/2log_a b=3x^2" "$ (substituting from $log_a b=x$ )

So

$x/2=3x^2$

$x=6x^2$

$6x=1$

$x=1/6$ with $x !=0$

Hence proved.

Answer 3 · 2018-06-03T18:38:56

We will start the proof

Explanation:

We have
$ln(a)/ln(b)=1/x$
and

$1/2*ln(b)/ln(a)=3x^2$
so

$ln(a)/ln(b)=1/(6x^2)$

using the first equation we get
$1/x=1/(6x^2)$

multiplying by $x^2$ we get

$x=1/6$ for $xne 0$

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If $log_ba=1/x and log_a √b =3x^2$ , show that x =1/6?

3 Answers

Explanation:

Explanation:

Explanation:

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Science

Math

Humanities

... and beyond

If log_ba=1/x and log_a √b =3x^2log_ba=1/x and log_a √b =3x^2, show that x =1/6?

3 Answers

Explanation:

Explanation:

Explanation:

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If $log_ba=1/x and log_a √b =3x^2$ , show that x =1/6?