Question

log√2base a =1/6 then a=?
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Answer 1

Answer:

logbase(a) root of(2) = 1/6

convert to:-

a^1/6 = squareroot 2

a = (sqrt2)^6

a = 8

Answer 2

Answer:

The value of a is 8.

Step-by-step explanation:

Given,

$\log _{a}^{\sqrt{2}}= \frac{1}{6}$

To find,

The value of 'a'

concept,

Some properties of the logarithmic function:

• If b = logₐⁿ then n = aᵇ...(1)
• ln(aˣ) = x ln (a)......(2)
• ln(ab)= ln(a)+ln(b)....(3)

Calculation,

$\log _{a}^{\sqrt{2}}= \frac{1}{6}$...(4)

Considering the L.H.S

i.e. $\log _{a}^{\sqrt{2}}$

using the property number (2) we can get,

$\log _{a}^{\sqrt{2}} = \frac{1}{2} \log_{a}^{2}$...(5)

Equating equations (5) and (4) we get:

1/2 logₐ² = 1/6

⇒ logₐ² = 1/3

Apllying the property (1) we get:

⇒ 2 = $a^{1/3}$

⇒ 8 = a

Therefore, the value of a is 8.

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