Basics Of Log Functions

0.5 can be written as 1/2 and further 1/2 can be written as ${ 2 }^{ -1 }$ .

So ${ 4 }^{ x }={ 2 }^{ -1 }\\ { 2 }^{ 2x }={ 2 }^{ -1 }$ therefore x=-1/2

$4^{x}=2^{2x}$ $0.5=\frac{1}{2}=2^{-1}$ $=> 2x=-1$ $=> x = -\frac{1}{2}$ $or$ $4^{x}=0.5$ $=> x\log 4 = \log 0.5$ $=> x=\frac{\log 0.5 }{\log 4}=-0.5$

log not required

multiuply both sides by 4

you get

${ 4 }^{ x+1 }$ = $=0.5\times4$

so,

${ 4 }^{ x+1 }$ = $2$

or,

${ 2 }^{ 2x+2 }$ = ${ 2 }^{ 1 }$

now, we solve for x

$2x+2=1$

$2x=-1$

$x=\frac { -1 }{ 2 }$

$x=\boxed{ -0.5 }$

$\frac { \log { 0.5 } }{ \log { 4 } } =\boxed{-0.5}$

4^x =0.5 or 2^2x=1/2 or 2^2x=2^-1 or x=-0.5

For those saying that calculating log(0.5)/log(4) requires a calculator.

log(0.5)=log(1/2)=log1-log2=-log2

And,

log(4)=log(2^2)=2log2

So,

log(0.5)/log(4)=-log2/(2log2)=-1/2

since 4^(x) = 0.5 2^(2x)=1/2 2^(2x+1)=1 therefore 2x+1=0 2x=-1 x=-0.5

{ 2 }^{ 2x }={ 2 }^{ -1 } =>2x=-1 =>x=-.5

1/sqrt(4) = 0.5, therefore x= -(1/2)

CORRECT ANSWER IS

-0.5

Take log on both side X log 4= log 0.5;
X=log .5/log 4;
X=-1/2. But its long version

4^x=0.5we can take both side x so,

  4^2x=0.5^x    
 (2^x) ^2=0.5^x          
 Now send 2^x to RHS and x will be left over
    x=(-2+0.5)^x
     x=-0.5

0.5=1/2 4^x=0.5 So, first we have to write 4^x in terms of 2 putting x=1/2, we get 2 We have to make it 182, so negative exponent of x gives 0.5 -x=1/2 x=-1/2=-0.5

2(4^x)=2(.5)

2(4^x)=1

first make it 1 then

1 / 2 = .5 and negative since it is an exponent. solve it this way. may be wrong

\sqrt{x}= x^{1/2}

0.5 = 1 / 2

4^{x} = 1/ 4^{-x}

1/2 = 1/4 ^{-1/2}

=> 2^2x = 2 ^ -1 => x=-0.5

4=2^2

so 4x = 2^2x = 0.5

0.5 = 1/2 which is reciprocal of 2 so 2x = -1

x = -0.5

x(log(4)) = log(0.5)

x = log(0.5) / log(4)

x = -0.5

4^x=0.5 4^x=1÷2 2 4^x=1 2 2^2x=2^0 2^(2x+1)=2^0 2x+1=0 X=-0.5

I admit i used the calculator. I was trying without using the calc mas some steps were missing. What can I do from -1 X log4 (2) = x?

You can use ln to separate x using log rules.

ln4^x = ln0.5

xln4 = ln0.5 (Use log rule that logA^B = BlogA)

x = ln0.5/ln4 (Requires calculator)

x=-0.5

multiply both sides by 4 ,,, so ,,,:-4 /\x+1=2,,, 4/\x+1=4/\1/2,,, x+1=1/2,,, x=-1/2

4^x=0.5,, 2^2x=2^-1,,

2x=-1,, x=-0.5

FIRST METHOD taking LOG in both sides, x log4 = log(1/2) x =log (1/2)/log4 having common base 2, then x =log4(1/2) (here 4 is base). =-1/2 =-0.5 second method is basics of surds.

Note that $0.5 = \frac {1}{2} = \frac {1}{2^1} = 2^{-1} = \left( 2^2 \right)^{-\frac{1}{2}} = 4^{\boxed{-0.5}}.$

4^x=.5 x=log(0.5)/log(4)

$Sine: 0.5 = 4^{-\frac{1}{2}} so => 4^{x} = 4^{-\frac{1}{2}}$ $=> Therefore: x = -\frac{1}{2} = \boxed{-0.5}$ !!!

4^x = 0.5

x = 4 log 1/2

= 2^2 log 2^-1 {sesuai sifat a^m log b^n = m/n(a log b)}

x = -1/2 = - 0.5

We can do this using logarithms too. We know that a ^ x = y implies x = log(y) to the base "a" . Here a=4 and y=0.5=1/2=2^(-1). So x = log(2 ^ ( -1)) to the base log(4). So x = -log(2)/log(4). So x = -log(2) / 2 * log(2) = -1/2 = -0.5

$4^{x} = 0.5$
$0.5= 1/2 =2^{-1}$
$4^{x} = 2^{2x}$
=> 2x= -1
=> x= -1/2 = -0.5

take log both side and get ans x log 4=log .5 x=-.5

4^x=1/2, take log to the base 2 on both sides, =>xlog 2^2=log 1 -log 2, 2x log 2= 0 - log2, 2x=-1, x=-0.5, here the base of the log is 2

Taking ln both side of the eqn. ln 4^x=ln(0.5), xln(4)=ln(0.5), x=ln(0.5)/ln(4), x=-0.5

ln4^x=ln(1/2) (Taking log both sides) ln 2^2x = ln 2^-1 2x ln2=-1ln2 now, 2x=-1 x=-1/2=-0.5

4 ^ (- x ) =1 / ( 4 ^ x ) -> 4 ^ 0. 5 = 2 -> 0.5 = 1/ 2 -> 4 ^ (-0.5) = 1 / ( 4 ^ 0.5 ) = 1 / 2 = 0.5

Since it belongs to the category of Logarithms, let's try it using log (whichever base). x*log(4)=log(0.5) x=log(4)/log(0.5) =-0.5

we know that a^b=x then->log x to the base a=b log 0.5 to the base 4=x =>log(1/2)/log 4=x =>(log1-log2)/log 4)=x =>(0-1)/2log2=x (log x^b=blog x) =>-1/2=x

Xlog4=log0.5

x=log0.5/log4

=-0.5

log0.5/log4

x = log0.5 / log4

take log on both sides and ul get, x=log(.5)/log(4)