How do you simplify #log10(sqrt10)#?

2 Answers
Leland Adriano Alejandro
Feb 18, 2016

the equivalent of the expression is #3/2#

Explanation:

We start from the given

#log 10sqrt10#

which also means

#log_10 10*sqrt10#

#log_10 10^1*10^(1/2)#

#log_10 10^((1+1/2))#

#log_10 10^(3/2)#

from the Laws of logarithms, we have
#log_b b^x=x#

so that the final simplification is simply

#3/2#

Noah G
Feb 19, 2016

#log10# means #log_10(10)#

Explanation:

#log_10(10)(sqrt(10))#

#log_aa = 1# because if you take the change of base rule #log_an = (logn/loga)#, with a and n being equal, the expressions cancel each other out, giving us 1.

=#1 xx sqrt(10)#

= #sqrt(10) or 2.16#

Practice exercises:

  1. Simplify #(log_3(3) / log_8(8))/sqrt(5)#. Don't forget to rationalize the denominator.

  2. Simplify #log_(x - 1)(x + 1) + log_(x + 1)(x - 1)#. Note: a helpful rule is: #log_an + log_am = log_a(n xx m)#

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