Question

Evaluate the expression without using a calculator: log10^3x-2y

Answer 1

`\huge\boxed{\log10^(3x-2y)=3x-2y}`

Explanation:

`\text{Use}\\\\(1)\log x=\log_(10)x\qquad(x>0)\\\\(2)\log_ab^n=n\log_ab\qquad(a>0;\ a\\eq1;\ b>0)\\\\(3)\log_aa=1\qquad(a>0;\ a\\eq1)\\\\\log10^(3x-2y)=\underbrace{(3x-2y)\log10}_((2))=\underbrace{(3x-2y)\log_(10)10}_((1))=\underbrace{(3x-2y)(1)}_((3))=3x-2y`

Answer 2

3x-2y

Explanation:

log10^(3x-2y)

We know the base is base 10 since it is not written

log10 10^(3x-2y)

The log10 10 cancels

3x-2y