gebuiteldmz

## Answered question

2022-09-06

Meaning of exponent in logarithm?
I have this particular difficulty :
${\mathrm{log}}_{b}^{a}\left(c\right)=x$
I know it is different from power of base ${\mathrm{log}}_{{b}^{a}}\left(c\right)=x$, but what does it actually mean?
The actual question that i got in paper was
Find value of
$\sqrt{{\mathrm{log}}_{0.5}^{2}8}$
And its answer was given as 3.

### Answer & Explanation

Helena Bentley

Beginner2022-09-07Added 10 answers

The exponent is a power, so you should read ${\mathrm{log}}_{b}^{a}\left(c\right)=x$ as $\left({\mathrm{log}}_{b}\left(c\right){\right)}^{a}=x$ In your specific case, ${\mathrm{log}}_{0.5}8=-3$, so when you square that you get 9 and when you take the square root you get get 3.

sengihantq

Beginner2022-09-08Added 3 answers

Well that pretty much means
$\left({\mathrm{log}}_{b}\left(c\right){\right)}^{a}$
In you case, it simplifies to
$\sqrt{\left({\mathrm{log}}_{0.5}8{\right)}^{2}}=|{\mathrm{log}}_{0.5}8|=|-3|=3$

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