What is the answer to (100)/(2+(0.75)^{2x)}=45 ?

The answer to (100)/(2+(0.75)^{2x)}=45 is x=(ln(2/9))/(2ln(0.75))

Solve for x: (100)/(2+(0.75)^{2x)}=45

The solution is x=(ln(2/9))/(2ln(0.75))

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\frac{100}{2 + ( 0.75 ) ^{2 x}} = 45

x = \frac{ln ( \frac{2}{9} )}{2 ln ( 0.75 )}

Decimal Notation

x = 2.61413 \dots

Solution steps

\frac{100}{2 + ( 0.75 ) ^{2 x}} = 45

Multiply both sides by

2 + 0.7 5^{2 x}

\frac{100}{2 + 0.7 5 ^{2 x}} (2 + 0.7 5^{2 x}) = 45 (2 + 0.7 5^{2 x})

Simplify

100 = 45 (2 + 0.7 5^{2 x})

Switch sides

45 (2 + 0.7 5^{2 x}) = 100

Divide both sides by

45

2 + 0.7 5^{2 x} = \frac{20}{9}

Move

2

to the right side

0.7 5^{2 x} = \frac{2}{9}

Apply exponent rules

2 x ln (0.75) = ln (\frac{2}{9})

Solve

2 x ln (0.75) = ln (\frac{2}{9}) : x = \frac{ln ( \frac{2}{9} )}{2 ln ( 0.75 )}

x = \frac{ln ( \frac{2}{9} )}{2 ln ( 0.75 )}

Verify Solutions:

x = \frac{ln ( \frac{2}{9} )}{2 ln ( 0.75 )}

True

The solution is

x = \frac{ln ( \frac{2}{9} )}{2 ln ( 0.75 )}

286.93 (0.973 8^{x}) = 15

e^{x - 3} = x - 1

e^{4 - 4 x} = 9

e^{2 x} = 12 + 11 e^{x}

343 (7^{2 x}) - 56 (7^{x}) + 1 = 0

What is the answer to (100)/(2+(0.75)^{2x)}=45 ?
The answer to (100)/(2+(0.75)^{2x)}=45 is x=(ln(2/9))/(2ln(0.75))
Solve for x: (100)/(2+(0.75)^{2x)}=45
The solution is x=(ln(2/9))/(2ln(0.75))