Question

if logx(9/16)=(-1/2),then x is equal to?

Answer 1

I hope the x is the base then this is the answer. Thanku

Answer 2

The value of x is 256/81.

Given:

• $log_{x}\left( \frac{9}{16} \right) = \frac{ - 1}{2}$

To find:

• Find the value of x.

Solution:

Concept/formula to be used:

• Take antilog.
• ${a}^{ - n} = \frac{1}{ {a}^{n} }$

Step 1:

Taking antilog both sides.

As, equation is

$log_{x}\left( \frac{9}{16} \right) = \frac{ - 1}{2}$

take antilog both sides.

$\frac{9}{16} = {x}^{ \frac{ - 1}{2} }$

Step 2:

Solve for x.

$\frac{9}{16} = \frac{1}{ \sqrt{x} }$

or

$\sqrt{x} = \frac{16}{9}$

squaring both sides

$\bf x = \frac{256}{81}$

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