2log4x+log4^4=3?

Answer 1

Using the laws

a*log(b)=log(b^a)
and
log(a)+log(b)=log(a*b)

we can get
log((4x)^2)+log(16)=3
log((16x)^2)=3
(16x)^2=1000

which can be solved with a calculator to give about x=1.97

note that i am assuming you meant a base 10 by simply stating log, and not a base e (which would be ln).

Answer 2

2log4x + log4^4 = 3
2log4x + 4log4 = 3
2log4x + 4(0∙602 59991..) = 3
2log4x + 2∙408 239 965 = 3
2log4x = 3 - 2∙408 239 965
2log4x = 0∙591 760 034...
log4x = 0∙591 760 034.../ 2 Take antilogs.
log4x = 0∙295 880 017...
4x = 1∙976 423 588....
x = 1∙976 423 588..../ 4
x = 0∙494 105 884 ....

Now, take this value and put it back into the original equation and you will see it balances out.

Answer 3

first thing eliminate the exponent in log4^4 by since log4^4 equal to 4log4

2log4x + log4^4=3
2log4x + 4log4 =3
now substitute both side by 4log4 since there are no unknowns in that number:

2log4x + 4log4 - 4log4 = 3 - 4log4
this gives you:

2log4x = 3 - 4log4

now divide both sids by 2log4

2log4x / 2log4 = (3 - 4log4) / 2log4
this gives you:

x = (3-4log4) / 2log4

Now simply work the equation: by tirst taking the logs of the numbers:
log4 = 0.6020 rounded off to four places

x = ( 3 - 4* 0.602) / 2* 06020

x = (3 - 2.408) / 1.204'

x = 0.592 / 1.204
x = 0.4917 to four places on decimal point:

now to check your answer:

2log4x + log4^4 = 3
2 * log (4*.4917) + 4 log 4 = 3
2 * log 1.9668 + 4 log 4 = 3
2 * 0.2937 + 4 * 0.6020 =3
0.5874 + 2.408 = 3
2.9954 = 3 which is due to rounding number off:
2.9954 when rounded off to zero decimal places will equal 3
so 3 =3
key factor here is that in the equation all numbers were at 0 decimal places:
to work number with calculator: using Ti 84 or casio fx 7000g

first simplify the equation to:

x = (3 - 4* log4) / 2+log4
on let's plug it in: {| |} denotes function keys to push:

( 3 {| - |} ( 4 {| x |} {| log |} 4 )) {/ divide key |} ( 2 {| x |} {| log |} 4 ) {|=|} answer 0.4914460712 before rounding off. put it in memory before rounding off:

to check answer: using calculator:

(2 {|*|} {|log|} (4 *MRL)) {| +|} ( 4 {|*|} {|log|} 4) = 2.995311684 which rounded off to zero decimal places gives you 3

Reason you have to use out to fourth deicmal place in answer even though there is no decimals in the problem is because your log base 10 tables are mostly based on four decimal places.

Answer 4

2log4x + log4^4 = 3

log (4x)^2 + log 256 = 3
log ( 16x^2 x 256 ) = 3
log ( 4096x^2 ) = 3
4096 x^2 = 1000
x^2 = 125/512
x = 0.4941

Answer 5

Square root of[ Anti-log(3)/(16*256)]

Answer 6

log(4x)^2 + log(16^2) = 3
log((4x)^2)16^2) =3
log(64x)^2 =3
2log(64x) =3
log64x =3/2
mean that
64x = 10^(3/2) then
x = sqrt(1000)/64 ^-^
x = 10sqrt(10)/64
= 5sqrt(10)/32