What is the answer to ln(2^x)+x=3 ?

The answer to ln(2^x)+x=3 is x= 3/(ln(2)+1)

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ln(2^x)+x=3

ln (2^{x}) + x = 3

x = \frac{3}{ln ( 2 ) + 1}

Decimal Notation

x = 1.77184 \dots

Solution steps

ln (2^{x}) + x = 3

Move

x

to the right side

ln (2^{x}) = 3 - x

f (x) = g (x),

then

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

e^{l n (2^{x})} = e^{3 - x}

Simplify

e^{l n (2^{x})} : 2^{x}

2^{x} = e^{3 - x}

Solve

2^{x} = e^{3 - x} : x = \frac{3}{ln ( 2 ) + 1}

x = \frac{3}{ln ( 2 ) + 1}

Verify Solutions:

x = \frac{3}{ln ( 2 ) + 1}

True

The solution is

x = \frac{3}{ln ( 2 ) + 1}

lo g_{10} (9 x) = \frac{3}{2}

lo g_{4} (3 x) - 1 = lo g_{4 - 2 + 9} (x)

- \frac{ln ( x ) - 1}{x ^{2}} = 0

- lo g_{10} (x) = 12.3

ln (x) = - 2 (0)^{2}