SOLUTION: what is the equation in logarithmic form for 16=(1/4)-2?

Question 950304: what is the equation in logarithmic form for 16=(1/4)-2?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe you mean 16 = (1/4)^(-2)

if you use your calculator to evaluate this equation, you will see that:

16 = 16.

this confirms the equation is true.

the ^ symbol indicates exponentiation.

the equation is 16 = (1/4)^-2

this is in the form of y = b^x, where:

y = 16
b = (1/4)
x = -2

in general, y = b^x if and only if log(b,y) = x

log(b,y) means log of y to the base of b.

apply that to your problem and you get:

16 = (1/4)^-2 if and only if log(1/4,16) = -2

how do you confirm?

use your calculator and the log conversion formula that tells you that:

log(1/4,16) = log(16) / log(1/4).

remember that log without mention of the base means the base is 10.

log(16) / log(1/4) means log of 16 to the base of 10 divided by log of 1/4 to the base of 10.

log to the base of 10 is the LOG function in your calculator.

your equation becomes:

log(16) / log(1/4) = -2

use your calculator to get:

-2 = -2

this confirms the conversion is correct.

RELATED QUESTIONS
(1/2)^4=1/16 write in logarithmic... (answered by stanbon)

Please write in logarithmic form... (answered by scott8148)

Write in logarithmic form... (answered by Alan3354)

144^1/2 Log144 12=1/2 What is the equation in logarithmic... (answered by tommyt3rd)

Rewrite the logarithmic equation log4/1/16=-2 in exponetial... (answered by stanbon)

Express the following logarithmic expression in exponential form 1. log 4 16-2 2.... (answered by user_dude2008)

Write the equation 4^-3 = 1/64 in logarithmic... (answered by fractalier)

Write the equation 4^-3= 1/64 in logarithmic form. (answered by jim_thompson5910)

Write the equation in logarithmic form: log4 (1/256)=-4 (answered by ewatrrr,MathTherapy)