What is the answer to 6.6=320(0.5)^{x/7} ?

The answer to 6.6=320(0.5)^{x/7} is x=(7ln(0.020625))/(ln(0.5))

Solve for x: 6.6=320(0.5)^{x/7}

The solution is x=(7ln(0.020625))/(ln(0.5))

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6.6 = 320 (0.5)^{\frac{x}{7}}

x = \frac{7 ln ( 0.020625 )}{ln ( 0.5 )}

Decimal Notation

x = 39.19623 \dots

Solution steps

6.6 = 320 (0.5)^{\frac{x}{7}}

Switch sides

320 \cdot 0. 5^{\frac{x}{7}} = 6.6

Divide both sides by

320

0. 5^{\frac{x}{7}} = 0.020625

Apply exponent rules

\frac{x}{7} ln (0.5) = ln (0.020625)

Solve

\frac{x}{7} ln (0.5) = ln (0.020625) : x = \frac{7 ln ( 0.020625 )}{ln ( 0.5 )}

x = \frac{7 ln ( 0.020625 )}{ln ( 0.5 )}

2^{x^{2 - 2}} = 4 x

9^{x - 1} = 5^{2 x - 2}

y = \frac{x}{e ^{x}}, x

e^{x - 3} = 2^{x - 1}

2 (9^{x}) - 7 (3^{x}) + 3 = 0

What is the answer to 6.6=320(0.5)^{x/7} ?
The answer to 6.6=320(0.5)^{x/7} is x=(7ln(0.020625))/(ln(0.5))
Solve for x: 6.6=320(0.5)^{x/7}
The solution is x=(7ln(0.020625))/(ln(0.5))