Question

Lg(log5(log(2)x))=0​

Answer 1

log5 (log(2)x=1

5log 2x= 10

log2x=2

2x=100

x=50

Answer 2

To solve the equation, we'll work step by step. First, let's simplify the equation:

LG(log₅(log₂(x))) = 0

Since LG is the base-10 logarithm, we can rewrite the equation as:

log₅(log₂(x)) = 0

Next, we'll use the property of logarithms that states: If logₐ(b) = c, then aᶜ = b.

So, in our equation, we have:

log₅(log₂(x)) = 0

This means that 5^0 should be equal to log₂(x):

5^0 = log₂(x)

Since any number raised to the power of 0 is always 1, we have:

1 = log₂(x)

Now, we need to rewrite this equation using the definition of logarithms:

logᵦ(a) = c if and only if ᵦᶜ = a

In our case:

log₂(x) = 1

This means:

2^1 = x

x = 2

So, the solution to the equation is x = 2.