given that log2 3 = x, log 2 5=y and log 2 7 = z, express log 2 21 in terms of x,y, and z
the 2 is the base
adding logs corresponds to multiplying numbers
so is it x+y
factors of 21?
can you just answer my question?
To express log2 21 in terms of x, y, and z, we can use logarithmic properties and relationships to rewrite it in a way that involves x, y, and z.
First, let's find the relationship between log2 21 and the given logarithmic expressions:
We know that 21 can be expressed as a product of prime numbers: 21 = 3 * 7.
Using the logarithmic property of the product, we can rewrite log2 21 as the sum of the logarithms of the individual prime factors:
log2 21 = log2 (3 * 7)
Using the logarithmic property of the power, we can separate the logarithm of a product into the sum of the logarithms of each factor:
log2 (3 * 7) = log2 3 + log2 7
Now, we will express each term using the given values:
log2 3 = x
log2 7 = z
Substituting these values into the expression for log2 21, we get:
log2 21 = log2 3 + log2 7
= x + z
Therefore, we can express log2 21 in terms of x, y, and z as x + z.