Question

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

Answer 1

Answer:

$\huge\boxed{\log10^{3x-2y}=3x-2y}$

Step-by-step explanation:

$\text{Use}\\\\(1)\log x=\log_{10}x\qquad(x>0)\\\\(2)\log_ab^n=n\log_ab\qquad(a>0;\ a\neq1;\ b>0)\\\\(3)\log_aa=1\qquad(a>0;\ a\neq1)\\\\\log10^{3x-2y}=\underbrace{(3x-2y)\log10}_{(2)}=\underbrace{(3x-2y)\log_{10}10}_{(1)}=\underbrace{(3x-2y)(1)}_{(3)}=3x-2y$

Answer 2

Answer:

3x-2y

Step-by-step 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