Use the Laws of logarithms to rewrite the expression log(1000000x^19)in a form with no logarithm of a product, quotient or power.
After rewriting we have log(1000000x^19)= A + Blog(x)?
I know B = 19, but what's A?
log(1000000x^19)
= log(10^6)+log(x^19)
= 6 + 19logx
assuming logs base 10 :-)
thank you!
To rewrite the expression log(1000000x^19) in a form with no logarithm of a product, quotient, or power, we can use the laws of logarithms.
The given expression can be written as the sum of two logarithms using the power rule:
log(1000000x^19) = log(1000000) + log(x^19)
Now, let's simplify each logarithm separately.
Using the product rule, we can simplify log(1000000) as follows:
log(1000000) = log(10^6)
Since log(10) = 1 (base 10 logarithm), we can substitute this in:
log(10^6) = 6log(10) = 6
Therefore, log(1000000) simplifies to 6.
Now, let's simplify log(x^19) using the power rule:
log(x^19) = 19log(x)
Now, we can rewrite the expression log(1000000x^19) as follows:
log(1000000x^19) = log(1000000) + log(x^19)
= 6 + 19log(x)
Therefore, we have log(1000000x^19) = 6 + 19log(x), which matches the format A + Blog(x).
In this case, A = 6 and B = 19.