## (-3)^(x-5)=-1/27 (-5)^(x+3)=-1/125 2*3^(x+2)+4*3^(x+1)=10*3^6 6*8^(x-1)+8^(x+1)=6*8^19+8^21

Question

(-3)^(x-5)=-1/27
(-5)^(x+3)=-1/125
2*3^(x+2)+4*3^(x+1)=10*3^6
6*8^(x-1)+8^(x+1)=6*8^19+8^21

in progress 0
1 year 2020-11-27T06:24:42+00:00 1 Answers 43 views 0

$\begin{array}{l} a){\left( { – 3} \right)^{x – 5}} = – \dfrac{1}{{27}}\\ \Rightarrow {\left( { – 3} \right)^{x – 5}} = \dfrac{1}{{{{\left( { – 3} \right)}^3}}}\\ \Rightarrow {\left( { – 3} \right)^{x – 5}} = {\left( { – 3} \right)^{ – 3}}\\ \Rightarrow x – 5 = – 3\\ \Rightarrow x = – 3 + 5 = 2\\ Vay\,x = 2\\ b){\left( { – 5} \right)^{x + 3}} = – \dfrac{1}{{125}}\\ \Rightarrow {\left( { – 5} \right)^{x + 3}} = {\left( { – 5} \right)^{ – 3}}\\ \Rightarrow x + 3 = – 3\\ \Rightarrow x = – 6\\ Vay\,x = – 6\\ c){2.3^{x + 2}} + {4.3^{x + 1}} = {10.3^6}\\ \Rightarrow {2.3^{x + 1}}.3 + {4.3^{x + 1}} = {10.3^6}\\ \Rightarrow {3^{x + 1}}.\left( {6 + 4} \right) = {10.3^6}\\ \Rightarrow {3^{x + 1}}.10 = {10.3^6}\\ \Rightarrow {3^{x + 1}} = {3^6}\\ \Rightarrow x + 1 = 6\\ \Rightarrow x = 5\\ Vay\,x = 5\\ d){6.8^{x – 1}} + {8^{x + 1}} = {6.8^{19}} + {8^{21}}\\ \Rightarrow {6.8^{x – 1}} + {8^{x – 1 + 2}} = {6.8^{19}} + {8^{19 + 2}}\\ \Rightarrow {8^{x – 1}}\left( {6 + {8^2}} \right) = {8^{19}}.\left( {6 + {8^2}} \right)\\ \Rightarrow {8^{x – 1}} = {8^{19}}\\ \Rightarrow x – 1 = 19\\ \Rightarrow x = 20\\ Vay\,x = 20 \end{array}$