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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