SOLUTION: Write the equations in logarithmic form. 216=6^3 36=(1/6)^(-2) a=bc

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Question 890348: Write the equations in logarithmic form.
216=6^3
36=(1/6)^(-2)
a=bc

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
logarithmic form os an exponential equation is as follows:

a^b = y if and only if loga(y) = b

your first equation is:

216 = 6^3

the logarithmic form of this equation would be log6(216) = 3

the base of the log is 6.


your second equation is:

36 = (1/6)^(-2)

without any modification to this equation, the logarithmic form would be log(1/6)(36) = -2

the base of the log is (1/6)

your third equation is:

a = b^c

the logarithmic form would be logb(a) = c

the base of the log is b.

for example:

let a = 36 and b = 6 and c = 2

you get a = b^c becoming 36 = 6^2

the log form of logb(a) = c becomes log6(36) = 2

you can use the base conversion formula to calculate this using your calculator.

you would get:

log10(36)/log10(6) = 2

now you can use your calculator to get:

2 = 2 confirming the calculations are good.

the conversation formula is:

loga(b) = logc(b) / logc(a)

the log of a number to a certain base tells you the exponent that the base has to be raised to in order to get the number.

example:

log10(1000) = 3

3 is the exponent that the base of 10 has to be raised to in order to get 1000.

that's where the identity comes in.

10^3 = 1000 if and only if log10(1000) = 3

log10(1000) = 3 if and only if 10^3 = 1000















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