gebuiteldmz

2022-09-06

Meaning of exponent in logarithm?

I have this particular difficulty :

$${\mathrm{log}}_{b}^{a}(c)=x$$

I know it is different from power of base ${\mathrm{log}}_{{b}^{a}}(c)=x$, 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.

I have this particular difficulty :

$${\mathrm{log}}_{b}^{a}(c)=x$$

I know it is different from power of base ${\mathrm{log}}_{{b}^{a}}(c)=x$, 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.

Helena Bentley

Beginner2022-09-07Added 10 answers

The exponent is a power, so you should read ${\mathrm{log}}_{b}^{a}(c)=x$ as $({\mathrm{log}}_{b}(c){)}^{a}=x$ 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

$$({\mathrm{log}}_{b}(c){)}^{a}$$

In you case, it simplifies to

$$\sqrt{({\mathrm{log}}_{0.5}8{)}^{2}}=|{\mathrm{log}}_{0.5}8|=|-3|=3$$

$$({\mathrm{log}}_{b}(c){)}^{a}$$

In you case, it simplifies to

$$\sqrt{({\mathrm{log}}_{0.5}8{)}^{2}}=|{\mathrm{log}}_{0.5}8|=|-3|=3$$

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