how would you simplify log10^x3 ?
i tried the examples from the book, but it just confuses me. someone please help.
log10(10^3) = 3
or you could put
log(10^3)=log(10)+log(10)+log(10)
which is 3xlog(10)
and as log(10)=1
so log(10^3)=3log(10)=3
I read that as
log10 10x3
= x^3(log 10)
= x^3
I wasn't sure as some of my students use 10^x3 when they mean 10^3. I think it goes with (incorrectly) using an extra x10 when putting powers of ten into a calculator.
To simplify log10^(x3), you need to use properties of logarithms. The given expression can be rewritten as log10(x^3) by applying the power rule of logarithms.
Here's how you simplify it step by step:
Step 1: Apply the power rule of logarithms:
log10(x^3) = 3·log10(x)
Step 2: Since log10(x) is a common logarithm (base 10), you can further simplify it to:
3·log10(x) = log10(x) + log10(x) + log10(x)
Step 3: Combine the logarithms:
log10(x) + log10(x) + log10(x) = log10(x · x · x)
Step 4: Simplify the multiplication:
log10(x · x · x) = log10(x^3)
Therefore, the simplified form of log10^(x3) is log10(x^3).