Question

If log, X = 0.5, then x is -

Answer 1

Answer:

Log(a)base (b) = 1/Log (b)base (a)

Similarly Log (4)base(x) = 1/Log (x)base (4)

Let Log (x)base (4) = y

So now we have 1/y + y = 5/2 = 10/4 = 2.5

1/y+y^2/y = 5/2

Now this is quadratic equation if we simplify this we get

y^2 — 5/2y + 1 = 0

This can be solved as all other quadratic equations are solved .

y=2 and also y=1/2

Now y=Log (x)base (4)

2=Log (x)base (4)

4^2=x (taking anti-log )

x=16

And also ,

y=1/2

1/2=Log (x)base (4)

4^1/2=x

(Root)4=x

x=2

x equals both 2 and 16.

Answer 2

Answer:

Concept :

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a fixed number, base b, must be raised in order to create a specific number x, is represented by the logarithm of that number. The logarithm, in its most basic form, counts the number of times the same factor appears when multiplied repeatedly; for instance, since 1000 = 10 x 10 x 10 = 103, its "logarithm base 10" is 3, or log10 (1000) = 3. When there is no possibility of mistake or when the base is irrelevant, as in big O notation, the logarithm of x to base b is written as logb (x), logb x, or even without the explicit base, log x.

Explanation:

Log x = 0.5

x =  log10 (0.5)

x = -0.3010

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