Exponent Relation Problem š„ Watch Video Solution Q. If \( 2^x = 3^y = 6^z \), find \( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \) (a) \( \frac{2}{x} \) (b) \( \frac{2}{y} \) (c) \( \frac{2}{z} \) (d) 1 āļø Solution \( 2^x = 3^y = 6^z = k \) \( x = […]
If 2^x = 3^y = 6^z, then 1/x = 1/y = 1/z = Read More Ā»
Minimum Value Problem š„ Watch Video Solution Q. If \( a^{b^c} = 6561 \), find least value of \( abc \) (a) 24 (b) 36 (c) 162 (d) none of these āļø Solution \( 6561 = 3^8 \) So \( a^{b^c} = 3^8 \) Take smallest base: \( a = 3 \Rightarrow
Maximum Value Problem š„ Watch Video Solution Q. If \( a^{b^c} = 256 \), find maximum value of \( abc \) (a) 12 (b) 16 (c) 32 (d) 256 āļø Solution \( 256 = 2^8 \) Possible forms: \( a^{b^c} = 2^8 \) Take \( a = 2 \Rightarrow b^c = 8
Exponent Evaluation š„ Watch Video Solution Q. If \( \sqrt{5^n} = 125 \), find \( 5^{\sqrt[n]{64}} \) (a) 25 (b) \( \frac{1}{125} \) (c) 625 (d) \( \frac{1}{5} \) āļø Solution \( (5^n)^{1/2} = 125 = 5^3 \) \( 5^{n/2} = 5^3 \Rightarrow n = 6 \) \( \sqrt[6]{64} = (2^6)^{1/6} =
If ā5^n =125, then 5^{nth root 64} = Read More Ā»
Exponent Equation š„ Watch Video Solution Q. If \( 16^{2x+3} = 64^{x+3} \), find \( 4^{2x-2} \) (a) 64 (b) 256 (c) 32 (d) 512 āļø Solution \( 16 = 2^4,\quad 64 = 2^6 \) \( (2^4)^{2x+3} = (2^6)^{x+3} \) \( 2^{8x+12} = 2^{6x+18} \) \( 8x + 12 = 6x +
If (16)^2x+3 = (64)^x+3, then 4^2x-2 = Read More Ā»
Exponent Evaluation š„ Watch Video Solution Q. If \( \sqrt{5^n} = 125 \), find \( 5^{\sqrt[n]{64}} \) (a) 25 (b) \( \frac{1}{125} \) (c) 625 (d) \( \frac{1}{5} \) āļø Solution \( (5^n)^{1/2} = 125 = 5^3 \) \( 5^{n/2} = 5^3 \Rightarrow n = 6 \) \( \sqrt[6]{64} = (2^6)^{1/6} =
If ā5^n = 125, then 5^{nā64} = Read More Ā»
Exponent Simplification š„ Watch Video Solution Q. \( 64^{-1/3}(64^{1/3} – 64^{2/3}) \) (a) 1 (b) \( \frac{1}{3} \) (c) -3 (d) -2 āļø Solution \( 64 = 2^6 \) \( 64^{1/3} = 4,\quad 64^{2/3} = 16 \) \( 64^{-1/3} = \frac{1}{4} \) \( = \frac{1}{4}(4 – 16) \) \( = \frac{1}{4}(-12) =
The value of 64^-1/3 (64^1/3 – 64^2/3), is Read More Ā»
Find x in Exponent Equation š„ Watch Video Solution Q. \( \frac{3^{2x-8}}{225} = \frac{5^3}{5^x} \) (a) 2 (b) 3 (c) 5 (d) 4 āļø Solution \( 225 = 3^2 \cdot 5^2 \) \( \frac{3^{2x-8}}{3^2 \cdot 5^2} = 5^{3-x} \) \( 3^{2x-10} \cdot 5^{-2} = 5^{3-x} \) \( 3^{2x-10} = 5^{5-x} \) Since
If (3^{2x-8})/225 = 5^3/5^x, than x = Read More Ā»
Exponent Simplification š„ Watch Video Solution Q. \( (256)^{-(4^{-3/2})} \) (a) 8 (b) \( \frac{1}{8} \) (c) 2 (d) \( \frac{1}{2} \) āļø Solution \( 4^{-3/2} = \frac{1}{4^{3/2}} = \frac{1}{(2^2)^{3/2}} = \frac{1}{2^3} = \frac{1}{8} \) \( (256)^{-(1/8)} = (2^8)^{-1/8} \) \( = 2^{-1} = \frac{1}{2} \) Correct Option: (d) \( \frac{1}{2} \)
When simplified (256)^{-(4^-3/2)} , is Read More Ā»
Find (2x)^x š„ Watch Video Solution Q. If \( 4^x – 4^{x-1} = 24 \), find \( (2x)^x \) (a) \( 5\sqrt{5} \) (b) \( \sqrt{5} \) (c) \( 25\sqrt{5} \) (d) 125 āļø Solution \( 4^x – 4^{x-1} = 24 \) \( = 4^{x-1}(4 – 1) = 24 \) \( 3
If4 ^x – 4^x-1 = 24, then (2x)^x equals Read More Ā»