how would I solve for 8^1/4 x (1/4)^x/2 = 16 ^3/4

Question

how would I solve for 8^1/4   x    (1/4)^x/2 = 16 ^3/4

anonymous · Answer

I think you have to use a log, but I have no clue. Anyone?

anonymous · Answer

I need to find the value for x I think

anonymous · Answer

and make bases the same

anonymous · Answer

What base would you use? I was never very good at log functions :(

anonymous · Answer

I would use 2

anonymous · Answer

but I dont know what to do after

anonymous · Answer

Ok, could you start by making everything in base 2?

anonymous · Answer

i did. and afer I got 2^3/4 x (1/2^2) ^ x/2 = 2^12/4

anonymous · Answer

Ok, now I'm as stuck as you are.

anonymous · Answer

:/

anonymous · Answer

Sorry, try to grab some attention from others who are good at logs.

anonymous · Answer

ok thanks anyways

campbell_st · Answer

just write them all as powers of 2$$(2^3)^{\frac{1}{4}} \times (2^{-2})^{\frac{x}{2}} = (2^4)^{\frac{3}{4}}$$

using index laws for power of a power and multiplication you get 

$$2^{\frac{3}{4} - x} = 2^3$$

so all you need to do is solve the equation 

3/4 - x = 3

anonymous · Answer

explain the index laws for power of a power and multiplication

anonymous · Answer

That's the part I don't remember :(

anonymous · Answer

okay I tried solving for what you gave me but couldn't get the right answer

tyteen4a03 · Answer

@teic85 Power of a power: (a^b)^c = a^ (bc)
Or a^b * a^c = a ^ (b+c)

no.identity05 · Answer

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x=2.25........ try to check my answer gyus