What is the answer to log_{2}(x+3)+log_{4}(5-x)=3 ?

The answer to log_{2}(x+3)+log_{4}(5-x)=3 is x=1,x=-1+2sqrt(5)

Solve for x: log_{2}(x+3)+log_{4}(5-x)=3

The solution is x=1,x=-1+2sqrt(5)

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lo g_{2} (x + 3) + lo g_{4} (5 - x) = 3

x = 1, x = - 1 + 25

Decimal Notation

x = 1, x = 3.47213 \dots

Solution steps

lo g_{2} (x + 3) + lo g_{4} (5 - x) = 3

Apply log rules

(x + 3)^{2} (5 - x) = 64

Solve

(x + 3)^{2} (5 - x) = 64 : x = 1, x = - 1 + 25, x = - 1 - 25

x = 1, x = - 1 + 25, x = - 1 - 25

Verify Solutions:

x = 1

True

, x = - 1 + 25

True

, x = - 1 - 25

False

The solutions are

x = 1, x = - 1 + 25

\frac{5 lo g _{2} ( x - 2 )}{3} = 6

lo g_{2} (x) + lo g_{2} (4 x) = 12

lo g_{8} (x - 8) + lo g_{8} (7) = 2

lo g_{a} (4) = 1.585, lo g_{a} (36)

lo g_{e} (x + 2) = 3

What is the answer to log_{2}(x+3)+log_{4}(5-x)=3 ?
The answer to log_{2}(x+3)+log_{4}(5-x)=3 is x=1,x=-1+2sqrt(5)
Solve for x: log_{2}(x+3)+log_{4}(5-x)=3
The solution is x=1,x=-1+2sqrt(5)