Question

How do you simplify `log10(sqrt10)`?

Answer 1

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`

Answer 2

`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)`