Question

log base 32 of (1/4) log base 32 of (1/4) @Mathematics

Answer 1

your job is to solve
\[32^{x}=\frac{1}{4}\] do you know it? i can show you how to cheat with a calculator if you like

Answer 2

no I don't know it. Please show me how to do it on a calculator

Answer 3

\[\log_{32}(\frac{1}{4})=x\]
satellite wrote this an exponential form

Answer 4

first how you do it without a calculator.
\[32=2^5\] and
\[\frac{1}{4}=2^{-2}\] so you can solve
\[5x=-2\] for x

Answer 5

\[x=\frac{\ln(\frac{1}{4})}{\ln(32)}=\frac{\ln(1)-\ln(4)}{\ln(32)}=\frac{0-\ln(4)}{\ln(32)}=-\frac{\ln(2^2)}{\ln(2^5)}\]
\[=-\frac{2 \cdot \ln(2)}{5 \cdot \ln(2)}=\frac{-2}{5}\]

Answer 6

i like satellite's way better

Answer 7

i used change of base formula

Answer 8

\[\log_b(x)=\frac{\ln(x)}{\ln(b)}\]

Answer 9

if you are going to use a calculator then just plug in myininaya's first line and type in
\[\ln(\frac{1}{4})\div\ln(32)\]

Answer 10

or even
\[\ln(.25)\div\ln(32)\] or
\[\log(,25)\div\log(32)\] but you are supposed to probably write my first answer on a test

Answer 11

I've never learned the change base formula so I'll probably stick with the first method. And thanks for the calculator method

Answer 12

yw

Answer 13

thats interesting
i wonder how your teacher expects you to enter it into the calculator
without knowing the change of base formula

Answer 14

that was my suggestion. i am fairly sure that the teacher wants jennifer to solve
\[32^x=\frac{1}{4}\]

Answer 15

ok

Answer 16

it is true. She doesn't want us to use calculators most of the time