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»
Find g for t = 64 š„ Watch Video Solution Q. If \( g = t^{\frac{2}{3}} + 4t^{-\frac{1}{2}} \), find \( g \) when \( t = 64 \) (a) \( \frac{31}{2} \) (b) \( \frac{33}{2} \) (c) 16 (d) \( \frac{257}{16} \) āļø Solution \( g = 64^{2/3} + 4 \cdot
If g = t^2/3 + 4t^-1/2 , what is the value of g when t = 64 ? Read More Ā»
Find x in Exponent Equation š„ Watch Video Solution Q. If \( \frac{x}{x^{1.5}} = 8x^{-1} \) and \( x > 0 \), find \( x \) (a) \( \frac{\sqrt{2}}{4} \) (b) \( 2\sqrt{2} \) (c) 4 (d) 64 āļø Solution \( \frac{x}{x^{1.5}} = x^{1 – 1.5} \) \( = x^{-0.5} \) \(
If x/x^1.5 = 8x^-1 and x greater than 0, then x = Read More Ā»
Find x^3 š„ Watch Video Solution Q. If \( x^2 = 2 \), find \( x^3 \) (a) \( \sqrt{2} \) (b) \( 2\sqrt{2} \) (c) \( 3\sqrt{2} \) (d) 4 āļø Solution \( x^2 = 2 \) \( x = \sqrt{2} \) (since x is positive) \( x^3 = x \cdot
If x is a positive real number and x^2 = 2, then x^3 (a) ā2 (b) 2ā2 (c) 3ā2 (d) 4 Read More Ā»
Find x in Exponent Equation š„ Watch Video Solution Q. If \( 9^{x+2} = 240 + 9^x \), find \( x \) (a) 0.5 (b) 0.2 (c) 0.4 (d) 0.1 āļø Solution \( 9^{x+2} = 9^x \cdot 9^2 \) \( = 81 \cdot 9^x \) \( 81 \cdot 9^x = 240 +
If 9^x+2 = 240 + 9^x, then x = (a) 0.5 (b) 0.2 (c) 0.4 (d) 0.1 Read More Ā»