log{b} 1000=3
I know b=10 but I don't understand how they got there.

Question

anonymous · Answer

$$\log_{b} 1000=3$$

anonymous · Answer

$$b^3=1000$$
$$3\sqrt{b^3}= 3\sqrt{1000}$$
b=10

nnesha · Answer

well did you take 3rd root right ?
you can write 1000 in terms of 3 exponents

nnesha · Answer

x^3 =1000 ?
what is x

anonymous · Answer

10

anonymous · Answer

What is the point of the 3's in front of the square root signs?

nnesha · Answer

that's not 3 it's a 3rd rooot i guess 
like this $$\huge\rm \sqrt[3]{b^3}$$

anonymous · Answer

Right, I didn't know how to do that

nnesha · Answer

you can convert 3rd to 1/3 exponent $$\huge\rm \sqrt[3]{b^3} = b^{3 \times \frac{ 1 }{ 3 }}$$ so cancel out 3 exponent u have to take 3rd root :=)

nnesha · Answer

$$\huge\rm \sqrt[3]{b^3} = b^{\cancel3 \times \frac{ 1 }{\cancel 3 }}=b$$

anonymous · Answer

Wouldn't that also mean that 1000 would be multiplied by 1/3?

nnesha · Answer

yes so 1000 can be written as 10 to the 3rd power $$\huge\rm \sqrt[3]{10^3}$$

anonymous · Answer

See that's where I get confused, so the 1000 get simplified down to 10 because?

nnesha · Answer

because it's easy to solve without calculator 
and it's legal :3

anonymous · Answer

-_- so because 10^3=1000 it gets simplified to 10^3 and since it's the 3rd root the exponent cancels out leaving b=10 ?

nnesha · Answer

b to the 3rd power so you can either write 10 to the 3rd power or put 3rd root of 1000 into the calculator :=)

nnesha · Answer

yep

anonymous · Answer

See when I enter that into my calc I get 94.86....

nnesha · Answer

and it's helpful when you  have to find an exponent 
given base 
for example 10^x = 1000

nnesha · Answer

what did you enter ?

freckles · Answer

$$3 \sqrt{1000} \neq \sqrt[3]{1000}$$

anonymous · Answer

$$3\sqrt{1000}$$

anonymous · Answer

Yea see I don't know how to enter the latter

nnesha · Answer

it's not 3  times square root of {1000}
3rd root like $$\sqrt[3]{1000}$$

nnesha · Answer

ohh then convert 3rd root to 1/3 exponent 
$$\huge\rm \sqrt[3]{1000} = (1000)^\frac{ 1 }{ 3 }$$

anonymous · Answer

That works. =] Could you possibly help me with another problem?

nnesha · Answer

gtg :3 sorry

anonymous · Answer

All's well Thank you for your help :)

nnesha · Answer

my pleasure