1) \[3^{4-5x}\times 3^{5x-4}= ?\]
Explanation:\[3^{4-5x+5x-4}= 3^{0}=1\](पाया समान म्हणून घातांकाची बेरीज)
2) \[37=3^{x}+3^{y}+3^{z}\: \: \: , \: x+y+z=?\]
Explanation: यामध्ये x, y, z च्या किमती अशा टाका की 3 चा तेवढ्या वेळा गुणाकार करून बेरीज केल्यास ती 37 येईल.
\[3^{x}+3^{y}+3^{z}\: \: = 3^{3}+3^{2}+3^{0}=?\]
= 27 + 9 + 1 = 37
x + y + z = 3 + 2 + 0 = 5
3) \[5^{6x+8}\div 5^{4x-5}=5^{21}\]
Explanation: यात भागाकार आहे म्हणून वजाबाकी करावे.
6x + 8 + (4x – 5) = 21
6x + 8 – 4x + 5 = 21
2x + 13 = 21
2x = 21 – 13
2x = 8
x = 4
4) \[\left ( \frac{15}{21} \right )^{12}\times \left ( \frac{15}{21} \right )^{14}\times \left ( \frac{21}{15} \right )^{26}\]
Explanation: \[\left ( \frac{15}{21} \right )^{12}\times \left ( \frac{15}{21} \right )^{14}\times \left ( \frac{21}{15} \right )^{-26}\: \\=\left ( \frac{15}{21}\right )^{12+14-26}\\\left ( \frac{12}{21} \right )^{0}=1\]
5) \[15^{3}\times \left ( 13^{3} \right )^{2}\times \left [ \left ( 15^{3} \right )^{2} \right ]^{2}=15^{m+8}\]
Explanation: \[15^{3}\times 15^{6}\times 15^{12}=15^{m+8}\]
\[m+8=21 \: \: 15^{21}=15^{m+8}\]
m = 21 – 8
m = 13
6) \[\frac{10^{0}+15^{0}+20^{0}}{10^{0}\times 15^{0}\times 20^{0}}=?\]
Explanation: \[\frac{1+1+1}{1\times 1\times 1}=\frac{3}{1}=3\]
7)\[\frac{5^{0}+6^{0}+7^{}}{5^{0}\times 6^{0}\times 7^{0}}=9^{x-3\: \: ,\: \: x=?}\\]\]
Explanation: \[\frac{1+1+7}{1\times 1\times 1}=\frac{9}{1}=9^{x-3}\: \\\\: 9=9^{x-3}\]1 = x-3
x =1 + 3 x = 4
8) \[\sqrt{6^{3x-2}}=6^{2}\: \: ,\: \: x=?\]
Explanation:दोन्ही बाजुंचा वर्ग करा\[\left ( \sqrt{6^{3x-2}} \right )^{2}= \left ( 6^{2} \right )^{2}\]\[6^{3x-2}=6^{4}\]
3x-2 = 4
3x = 4 + 2
3x = 6 x = 6⁄/3
x = 2
9) \[\frac{6^{2}\times 36\times 6^{4}}{36^{2}\times 6}=6^{x+1}\: \: , x=?\]
Explanation: \[\frac{6^{2}\times 6^{2}\times 6^{4}}{\left ( 6^{2} \right )^{2}\times 6}= \: \: \: \left (36=6^{2} \right )\] \[\frac{6^{8}}{6^{5}}\:=6^{x+1}\: \: \: \: \frac{6^{2}\times 6^{2}\times 6^{4}}{\left ( 6^{4} \right )\times 6}=6^{6x+1}\] \[6^{3}=6^{6x+1}\] 3 = x + 1 x = 3 – 1 x = 2
10) \[\sqrt{256^{\frac{1}{2}}}= m\:, \: \:m=?\]
Explanation: \[\sqrt{256^{\frac{1}{2}}}= (\frac{1}{2}=\] घातांक आहे वर्गमुळ)\[\sqrt{16}=4\]