Question

How would you rewrite *1000^log(x)* as an expression of x which does not involve any logs??

Answer 1

There is a property of logs that is based directly on the definition and is very useful here:\[b^{\log_{b}(x)}=x \]First rewrite 1000 to a power of 10\[1000^{\log(x)}=(10^3)^{\log(x)}\]Now we know that a base to a power, raised to a power is a product\[=10^{3 \log(x)}\]Now commute the factors in the exponent\[=10^{\log(x)*3}\]and then use the property from the start of this post to rewrite the base as x\[=x^3\]And this is your simplified form.