What is the answer to 6^{2x}-6^x-30=0 ?

The answer to 6^{2x}-6^x-30=0 is x=1

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6^{2x}-6^x-30=0

6^{2 x} - 6^{x} - 30 = 0

x = 1

Solution steps

6^{2 x} - 6^{x} - 30 = 0

Apply exponent rules

(6^{x})^{2} - 6^{x} - 30 = 0

Rewrite the equation with

6^{x} = u

(u)^{2} - u - 30 = 0

Solve

u^{2} - u - 30 = 0 : u = 6, u = - 5

u = 6, u = - 5

Substitute back

u = 6^{x},

solve for

x

Solve

6^{x} = 6 : x = 1

Solve

6^{x} = - 5 :

No Solution for

x \in R

x = 1

2. 5^{x - 3} = 6.25

(e^{5})^{3 x} = e^{5} e^{3 x}

5^{2 x - 16} = 2 5^{3 x + 2}

4^{x^{2}} \cdot 2^{5 x} = 8

7 e^{5 x + 4} = 6