What is the answer to (25^x+125)/6 =5^{x+1} ?

The answer to (25^x+125)/6 =5^{x+1} is x=2,x=1

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(25^x+125)/6 =5^{x+1}

\frac{2 5 ^{x} + 125}{6} = 5^{x + 1}

x = 2, x = 1

Solution steps

\frac{2 5 ^{x} + 125}{6} = 5^{x + 1}

Multiply both sides by

6

\frac{2 5 ^{x} + 125}{6} \cdot 6 = 5^{x + 1} \cdot 6

Simplify

2 5^{x} + 125 = 5^{x + 1} \cdot 6

Apply exponent rules

(5^{x})^{2} + 125 = 5^{x} \cdot 5^{1} \cdot 6

Rewrite the equation with

5^{x} = u

(u)^{2} + 125 = u \cdot 5^{1} \cdot 6

Solve

u^{2} + 125 = u \cdot 5^{1} \cdot 6 : u = 25, u = 5

u = 25, u = 5

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 25 : x = 2

Solve

5^{x} = 5 : x = 1

x = 2, x = 1

1 0^{x} = 200

8 (2^{2 x}) - 65 (2^{x}) + 8 = 0

1000000 = 2^{n} \cdot 5^{n}

6 4^{x} - 8 = 7 (4^{x} - 2)

3^{x} = x^{2}

What is the answer to (25^x+125)/6 =5^{x+1} ?
The answer to (25^x+125)/6 =5^{x+1} is x=2,x=1
Solve for x: (25^x+125)/6 =5^{x+1}
The solution is x=2,x=1