What is the answer to 16^x-5*4^x=24 ?

The answer to 16^x-5*4^x=24 is x= 3/2

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16^x-5*4^x=24

1 6^{x} - 5 \cdot 4^{x} = 24

x = \frac{3}{2}

Decimal Notation

x = 1.5

Solution steps

1 6^{x} - 5 \cdot 4^{x} = 24

Apply exponent rules

(4^{x})^{2} - 5 \cdot 4^{x} = 24

Rewrite the equation with

4^{x} = u

(u)^{2} - 5 u = 24

Solve

u^{2} - 5 u = 24 : u = 8, u = - 3

u = 8, u = - 3

Substitute back

u = 4^{x},

solve for

x

Solve

4^{x} = 8 : x = \frac{3}{2}

Solve

4^{x} = - 3 :

No Solution for

x \in R

x = \frac{3}{2}

3^{2 c + 1} = 28 \cdot 3^{c} - 9

9^{x^{2} - x - 4} = 3^{6 x + 2}

2^{2 x} + 2^{x} = 12

x, 3^{x} - 9 y + 113 = 6 y^{4}

m^{m} = \frac{1}{2}