Question

Find the value of x, if (16)^245 = (32)^x​

Answer 1

Answer:

192=3∗64192=3∗64

Step-by-step explanation:

2x+2x+2x2x+2x+2x is the same thing as 3∗2x3∗2x (this is pretty much the definition of multiplication with integers.) Also, 192=3∗64192=3∗64 (if you're not a nerd like me you would do that with a calculator). So you have 3∗2x=3∗643∗2x=3∗64 . You should be able to tell that 2x=642x=64 from this, although that's actually fairly complicated to prove if you wanna go all Peano about it (which I'm assuming you don't because otherwise you probably would have included that in the questions.) Now you're gonna wanna take the log base 2 of both sides for reasons that will become apparent in a moment. log22x=log264log2⁡2x=log2⁡64 . log22xlog2⁡2x is just xx since logarithms are designed to be the inverse function for raising numbers to the power of x. log264log2⁡64 is just 6 ; you can do that with a calculator if you don't remember that 26=6426=64 . If your calculator doesn't have a button for logxylogx⁡y , you can put in ln(x)/ln(y)ln(x)/ln(y) or log(x)/log(y)log(x)/log(y) and that should do the same thing. Putting that all together we have log22x=log264=>x=log264=>x=6log2⁡2x=log2⁡64=>x=log2⁡64=>x=6 and we're done

Answer 2

Answer:

16=2^4and32=2^5.

(x^y) ^z=x^y*z

question:(2^4)^245=2^5^x.

2^4*245=2^980.

2^980=2^5^x.

now, we have to find value of x. which is equal to 980/5.because^5^x=^5x.so ^x=980/5.=196.

answer -16^245=32^x.and x=196.