What is the answer to 123456789=3.5(0.9825)^x ?

The answer to 123456789=3.5(0.9825)^x is x=(ln(246913578/7))/(ln(0.9825))

Solve for x: 123456789=3.5(0.9825)^x

The solution is x=(ln(246913578/7))/(ln(0.9825))

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123456789 = 3.5 (0.9825)^{x}

x = \frac{ln ( \frac{246913578}{7} )}{ln ( 0.9825 )}

Decimal Notation

x = - 984.35018 \dots

Solution steps

123456789 = 3.5 (0.9825)^{x}

Switch sides

3.5 \cdot 0.982 5^{x} = 123456789

Multiply both sides by

10

35 \cdot 0.982 5^{x} = 1234567890

Divide both sides by

35

0.982 5^{x} = \frac{246913578}{7}

Apply exponent rules

x ln (0.9825) = ln (\frac{246913578}{7})

Solve

x ln (0.9825) = ln (\frac{246913578}{7}) : x = \frac{ln ( \frac{246913578}{7} )}{ln ( 0.9825 )}

x = \frac{ln ( \frac{246913578}{7} )}{ln ( 0.9825 )}

y, (5^{- 1})^{3} = x^{y}

4 + 5 e^{x + 2} = 11

3 6^{x + 1} = 6^{x}

e^{x + 5} = 2

\frac{2 ^{- 2 x}}{3 ^{2 x}} = 9^{- x}

What is the answer to 123456789=3.5(0.9825)^x ?
The answer to 123456789=3.5(0.9825)^x is x=(ln(246913578/7))/(ln(0.9825))
Solve for x: 123456789=3.5(0.9825)^x
The solution is x=(ln(246913578/7))/(ln(0.9825))