What is the answer to 25=(100(0.5)^t)/(5730) ?

The answer to 25=(100(0.5)^t)/(5730) is t=(ln(2865/2))/(ln(0.5))

Solve for t: 25=(100(0.5)^t)/(5730)

The solution is t=(ln(2865/2))/(ln(0.5))

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25 = \frac{100 ( 0.5 ) ^{t}}{5730}

t = \frac{ln ( \frac{2865}{2} )}{ln ( 0.5 )}

Decimal

t = - 10.48431 \dots

Solution steps

25 = \frac{100 ( 0.5 ) ^{t}}{5730}

Multiply both sides by

5730

25 \cdot 5730 = \frac{100 \cdot 0. 5 ^{t}}{5730} \cdot 5730

Simplify

143250 = 100 \cdot 0. 5^{t}

Switch sides

100 \cdot 0. 5^{t} = 143250

Divide both sides by

100

0. 5^{t} = \frac{2865}{2}

Apply exponent rules

t ln (0.5) = ln (\frac{2865}{2})

Solve

t ln (0.5) = ln (\frac{2865}{2}) : t = \frac{ln ( \frac{2865}{2} )}{ln ( 0.5 )}

t = \frac{ln ( \frac{2865}{2} )}{ln ( 0.5 )}

2 (7^{x}) = 686

9^{- x} = 27

81 (3^{x^{2} + 5 x}) = 243

1 1^{2 x + 1} = 11

49 e^{7 x} + e^{- x} = 0

What is the answer to 25=(100(0.5)^t)/(5730) ?
The answer to 25=(100(0.5)^t)/(5730) is t=(ln(2865/2))/(ln(0.5))
Solve for t: 25=(100(0.5)^t)/(5730)
The solution is t=(ln(2865/2))/(ln(0.5))