# Thread: 5 ^ x-2+log 4(base 5)=20 find x?

1. ## 5 ^ x-2+log 4(base 5)=20 find x?

also for 2logx^2 (base 3) + 2log(3 sqrt x) (base 3) =7 i got x=1.65 is this correct

the first question is 5 ^ (x-2+log 4(base 5))=20 find x? sorry
thanks

2. Originally Posted by b0mb3rz
also for 2logx^2 (base 3) + 2log(3 sqrt x) (base 3) =7 i got x=1.65 is this correct
???

$\displaystyle 2\log_3x^2+2\log_33\sqrt x=7$

$\displaystyle \Rightarrow\log_3x^4+\log_39x=7$

$\displaystyle \Rightarrow\log_3\left[x^4(9x)\right]=7$

$\displaystyle \Rightarrow\log_39x^5=7$

$\displaystyle \Rightarrow9x^5=3^7$

$\displaystyle \Rightarrow x^5=3^5$

$\displaystyle \Rightarrow x=3.$

the first question is 5 ^ (x-2+log 4(base 5))=20 find x? sorry
thanks
$\displaystyle 5^{x-2+\log_54}=20$

$\displaystyle \Rightarrow5^x5^{-2}5^{\log_54}=20$

Can you finish it?

3. does this simplify to

4( 5^x 5^-2) = 20
therefore x=3???

4. Originally Posted by b0mb3rz

does this simplify to

4( 5^x 5^-2) = 20
therefore x=3???
Correct.

$\displaystyle 4\cdot5^x5^{-2}=20$

$\displaystyle \Rightarrow5^x5^{-2}=5$

$\displaystyle \Rightarrow5^x=125$

$\displaystyle \Rightarrow x=3$