5-5-3x-2-x-5-5-7-3x-2-x-6-

Question Number 99050 by bemath last updated on 18/Jun/20

5^{5 - 3 x} + 2^{x + 5} = 5^{7 - 3 x} - 2^{x + 6}

Commented by bobhans last updated on 18/Jun/20

\frac{5^{5}}{5^{3 x}} + 32 . 2^{x} = \frac{5^{7}}{5^{3 x}} - 64 . 2^{x}

96 . 2^{x} = \frac{5^{5} (5^{2} - 1)}{5^{3 x}} = \frac{24 . 5^{5}}{5^{3 x}}

4 . 2^{x} = 5^{5 - 3 x} \Rightarrow 2^{2 + x} = 5^{5 - 3 x}

(2 + x) \ln (2) = (5 - 3 x) \ln (5)

x \ln (2) + 3 x \ln (5) = 5 \ln (5) - 2 \ln (2)

x (0.693 + 4.828) = 8.047 - 1.386

x = \frac{6.661}{5.521} \approx 1.206

Commented by bemath last updated on 18/Jun/20

thank you both sir

Answered by Rasheed.Sindhi last updated on 18/Jun/20

5^{5 - 3 x} + 2^{x + 5} = 5^{7 - 3 x} - 2^{x + 6}

2^{x + 5} + 2^{x + 6} = 5^{7 - 3 x} - 5^{5 - 3 x}

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

\frac{2^{x + 5} \times 5^{3 x}}{5^{5}} = \frac{24}{3}

2^{5} . 2^{x} . 125^{x} = \frac{24 . 5^{5}}{3}

{(250)}^{x} = \frac{24 . 5^{5}}{3 . 2^{5}}

{(250)}^{x} = \frac{8 . 5^{5}}{2^{5}} = \frac{5^{5}}{2^{2}}

x = \frac{5 \log 5 - 2 \log 2}{\log 250} \approx 1.2064