Question

Log base 10(log base 10(log base 10x)=0,then value of x is?

Answer 1

Given

we have given log₁₀(log₁₀(log₁₀ₓ)=0

To Find

we have to find value of x

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Now ,we see that all log are in product form

So,we first open the brackets and simply multiply the log :

=>log₁₀×log₁₀×log₁₀ₓ=0

logarithmic properties:

Log m × log n= logm + log n

log₁₀×log₁₀ can also be written as log²₁₀ = 2log₁₀=log₁₀+log₁₀

=>log₁₀+log₁₀×log₁₀ₓ=0

=>log₁₀+(log₁₀+log₁₀ₓ)=0

=>log₁₀+log₁₀+log₁₀ₓ=0

=>2log₁₀= -log₁₀ₓ

For two functions to be be equal the arguments of that function must be equal.

So,the exact value for x will be

x= 1/1000

or x = 0.001

Other logarithmic properties:

• log m-logn = logm÷ logn
• log base e = 1
• log 1 = 0