log { base 3 } of [ log { base 2 } of ( 2x - 1 ) ] = ...

[Secret]

Hii

umm ..

I have this problem and I solved it

but I'm not really sure if the answer was correct

so I just want you to tell me if it's correct or not

and if it wasn't correct .. maybe you can help me find the correct answer


well this is the problem


log { base 3 } of [ log { base 2 } of ( 2x - 1 ) ] = log { base 2 } of 4

so

log { base 3 } of [ log { base 2 } of ( 2x - 1 ) ] = 2

3^2 = log { base 2 } of ( 2x - 1 )

log { base 2 } of ( 2x - 1 ) = 9

2x - 1 = 2^9

2x = 512 + 1

2x = 513

x = 513/2

x = 256.5


is my answer correct ?!

 

[soroban]

Re: logarithms =]

Hello, Secret!

If you will use [ color=beige ], we won't be able to read the problem AT ALL . . .

\(\displaystyle \log_3\left[\log_2(2x\.-\.1)\right] \:= \:\log_2(4)\)

so: \(\displaystyle \:\log_3\left[\log_2(2x\,-\,1 )\right]\:=\:2\)

. . \(\displaystyle 3^2 \:= \:\log_2(2x\,-\,1)\)

. . \(\displaystyle \log_2(2x\,-\,1) \:=\: 9\)

. . \(\displaystyle 2x\,-\,1 \:= \:2^9\)

. . \(\displaystyle 2x\,-\,1 \:= \:512\)

. . \(\displaystyle 2x \:= \:513\)

. . \(\displaystyle x \:= \:\frac{513}{2}\)

. . \(\displaystyle x \:= \:256.5\)

is my answer correct ? . . . . Yes!

Did you check your answer?

Let \(\displaystyle x\,=\,256.5\)
. . We know that the right side of the equation is \(\displaystyle 2.\)

We have: \(\displaystyle \:\log_3\left(\log_2[2(256.5)\,-\,1]\right) \;=\;2\;\) . . . Is this true?

The left side is: \(\displaystyle \:\log_3\left(\log_2(512)\right) \;=\;\log_3(9) \;=\;2\;\) . . . Yes!

 

[Secret]

cool


so my answer is correct