What is the answer to solvefor x,t(x)=log_{4}(x+2) ?

The answer to solvefor x,t(x)=log_{4}(x+2) is x=-(\W(-\frac{2ln(2)t)/(16^t))+4ln(2)t}{2ln(2)t}

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solvefor x,t(x)=log_{4}(x+2)

solve for

x, t (x) = lo g_{4} (x + 2)

x = - \frac{W ( - \frac{2 l n ( 2 ) t}{1 6 ^{t}} ) + 4 ln ( 2 ) t}{2 ln ( 2 ) t}

Solution steps

t (x) = lo g_{4} (x + 2)

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

4^{t x} = 4^{l o g_{4} (x + 2)}

Simplify

4^{l o g_{4} (x + 2)} : x + 2

4^{t x} = x + 2

Solve

4^{t x} = x + 2 : x = - \frac{W ( - \frac{2 l n ( 2 ) t}{1 6 ^{t}} ) + 4 ln ( 2 ) t}{2 ln ( 2 ) t}

x = - \frac{W ( - \frac{2 l n ( 2 ) t}{1 6 ^{t}} ) + 4 ln ( 2 ) t}{2 ln ( 2 ) t}

Verify Solutions:

x = - \frac{W ( - \frac{2 l n ( 2 ) t}{1 6 ^{t}} ) + 4 ln ( 2 ) t}{2 ln ( 2 ) t}

True

The solution is

x = - \frac{W ( - \frac{2 l n ( 2 ) t}{1 6 ^{t}} ) + 4 ln ( 2 ) t}{2 ln ( 2 ) t}

ln (x) = \frac{3}{2}

ln (x^{2}) = 0

lo g_{a} (8) = 6

0 = - ln (- x)

ln (x + 2) + ln (3) = 5

What is the answer to solvefor x,t(x)=log_{4}(x+2) ?
The answer to solvefor x,t(x)=log_{4}(x+2) is x=-(\W(-\frac{2ln(2)t)/(16^t))+4ln(2)t}{2ln(2)t}