Question

log0.01^10

what is value?​

Answer 1

$= log(0.01) {}^{10} \\ = log( {10}^{ - 2} ) {}^{10} \\ = log( {10}^{ - 20} ) \\ = - 20 \\ \\ \\ mark \: \: brainliest \: ...$

Answer 2

Answer:

-20

Step-by-step explanation:

$\log a=\log_{10}a;\ \text{for}\ a>0\\\\\log_ab^n=n\log_ab,\ \text{for}\ a\neq1\ \wedge\ a>0\ \wedge\ b>0\\\\\log_aa=1,\ \text{for}\ a>0\ \wedge\ a\neq1\\\\a^{-n}=\dfrac{1}{a^n},\ \text{for}\ a\neq0\\\\==========================$

$\log0.01^{10}=10\log0.01=10\log\dfrac{1}{100}=10\log\dfrac{1}{10^2}=10\log10^{-2}\\\\=(-2)(10)\log10=-20\cdot1=-20$