One last log law question. little more trickier.

[Senjai]

Homework Statement

$$10^{log_{100}4}$$ Evaluate.

I'm on a school computer, i cannot see TEX images. Sorry if their not 100% correct.[/color]

The Attempt at a Solution

I solved this answer, and got 2. i did this by making the above equation:

$$100^\frac{1}{2}(log_{100}4)$$
then using a log law to get 4 to the power of 1/2 and solved for 2 using the "double base rule"

I was told their was a way to do the same thing, but for the exponent and not the base.

how do you solve: $$10^{log_{10^2}4}$$ somehow it still gives a power of 1/2 to the value 4 but i don't understand how to put it there.

i tried putting it in exponential form:

$$10^{2x} = 4$$

and i guess ed by dividing both exponents by 2 to get:

$$10^x = 4^{\frac{1}{2}}$$

but 10 and 4 arent the same base. Is this correct?

Thanks,
Senjai

 

[Donaldos]

Maybe you can use the identity:

$$\log_{100} x=\frac{\log_{10} x}{\log_{10} 100}$$

?

 

[Mark44]

And in Donaldos's formula, log₁₀100 = 2.