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Popular >

4(2/3)^{x^2-5x+4}=9

Solution

4 (\frac{2}{3})^{x^{2} - 5 x + 4} = 9

Solution

x = - \frac{- 5 ln ( \frac{2}{3} ) - 9 ln ^{2} ( \frac{2}{3} ) + 4 ln ( \frac{2}{3} ) ln ( \frac{9}{4} )}{2 ln ( \frac{2}{3} )}, x = - \frac{9 ln ^{2} ( \frac{2}{3} ) + 4 ln ( \frac{2}{3} ) ln ( \frac{9}{4} ) - 5 ln ( \frac{2}{3} )}{2 ln ( \frac{2}{3} )}

+1

Solution steps

4 (\frac{2}{3})^{x^{2} - 5 x + 4} = 9

Divide both sides by

4

(\frac{2}{3})^{x^{2} - 5 x + 4} = \frac{9}{4}

Apply exponent rules

(x^{2} - 5 x + 4) ln (\frac{2}{3}) = ln (\frac{9}{4})

Solve

(x^{2} - 5 x + 4) ln (\frac{2}{3}) = ln (\frac{9}{4}) : x = - \frac{- 5 ln ( \frac{2}{3} ) - 9 ln ^{2} ( \frac{2}{3} ) + 4 ln ( \frac{2}{3} ) ln ( \frac{9}{4} )}{2 ln ( \frac{2}{3} )}, x = - \frac{9 ln ^{2} ( \frac{2}{3} ) + 4 ln ( \frac{2}{3} ) ln ( \frac{9}{4} ) - 5 ln ( \frac{2}{3} )}{2 ln ( \frac{2}{3} )}

x = - \frac{- 5 ln ( \frac{2}{3} ) - 9 ln ^{2} ( \frac{2}{3} ) + 4 ln ( \frac{2}{3} ) ln ( \frac{9}{4} )}{2 ln ( \frac{2}{3} )}, x = - \frac{9 ln ^{2} ( \frac{2}{3} ) + 4 ln ( \frac{2}{3} ) ln ( \frac{9}{4} ) - 5 ln ( \frac{2}{3} )}{2 ln ( \frac{2}{3} )}

Popular Examples

e^{k x} = 0

2^{x-1}+1/(2^{x-3)}=5

2^{x - 1} + \frac{1}{2 ^{x - 3}} = 5

7 \cdot e^{0.1 t} = 47

e^{7 - 4 x} = 5

2^{2x}-12*2^x+32=0

2^{2 x} - 12 \cdot 2^{x} + 32 = 0

Frequently Asked Questions (FAQ)

What is the answer to 4(2/3)^{x^2-5x+4}=9 ?
The answer to 4(2/3)^{x^2-5x+4}=9 is
Solve for x: 4(2/3)^{x^2-5x+4}=9
The solution is