What is the answer to 5^{x-3}+125^{x+3}=78125 ?

The answer to 5^{x-3}+125^{x+3}=78125 is x=-0.66666…

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5^{x-3}+125^{x+3}=78125

5^{x - 3} + 12 5^{x + 3} = 78125

x = - 0.66666 \dots

Solution steps

5^{x - 3} + 12 5^{x + 3} = 78125

Apply exponent rules

5^{x} \cdot 5^{- 3} + (5^{x})^{3} \cdot 5^{9} = 78125

Rewrite the equation with

5^{x} = u

u \cdot 5^{- 3} + (u)^{3} \cdot 5^{9} = 78125

Solve

u \cdot 5^{- 3} + u^{3} \cdot 5^{9} = 78125 : u \approx 0.34199 \dots

u \approx 0.34199 \dots

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 0.34199 \dots : x = - 0.66666 \dots

x = - 0.66666 \dots

2^{3000} = 1 0^{x}

(\frac{1}{2})^{n} + 1 = 2

t, 4 \frac{( x ^{2} ) ^{- t}}{5} = 288

2^{x} + 3 \cdot 2^{x} = 16

x, \frac{( 9 ^{x - 1} )}{( 3 ^{y + 2} )} = 81

What is the answer to 5^{x-3}+125^{x+3}=78125 ?
The answer to 5^{x-3}+125^{x+3}=78125 is x=-0.66666…
Solve for x: 5^{x-3}+125^{x+3}=78125
The solution is x=-0.66666…