Advertisements
Advertisements
Question
If 4x + 3 = 112 + 8 × 4x, find the value of (18x)3x.
Advertisements
Solution
4x + 3 = 112 + 8 × 4x
⇒ 4x x 43 = 112 + 8 x 4x
⇒ 64 x 4x = 112 + 8 x 4x
Let 4x = y
64y = 112 + 8y
⇒ 56y = 112
⇒ y = 2
Substituting We get,
4x = 2
⇒ 22x = 2
⇒ 2x = 1
⇒ x = `1/2`
`( 18x )^(3x) = (18/2)^( 3 xx 1/2 ) = 9^( 3 xx 1/2 ) = ( 9^(1/2))^3 = 3^3 = 27`
APPEARS IN
RELATED QUESTIONS
Solve for x: `4^(x-1) × (0.5)^(3 - 2x) = (1/8)^-x`
Solve for x:
`(81)^(3/4) - (1/32)^(-2/5) + x(1/2)^(-1).2^0 = 27`
If ax = by = cz and b2 = ac, prove that: y = `[2xz]/[x + z]`
Evaluate the following:
`(12^2 xx 75^-2 xx 35 xx 400)/(48^2 xx 15^-3 xx 525)`
Evaluate the following:
`(8/27)^((-2)/3) - (1/3)^-2 - 7^0`
Evaluate the following:
`16^(3/4) + 2(1/2)^-1 xx 3^0`
Find the value of k in each of the following:
`(root(3)(8))^((-1)/(2)` = 2k
If x = `3^(2/3) + 3^(1/3)`, prove that x3 - 9x - 12 = 0
Prove the following:
`(x^("a"+"b")/x^"c")^("a"-"b") · (x^("c"+"a")/(x^"b"))^("c"-"a") · ((x^("b"+"c"))/(x"a"))^("b"-"c")` = 1
Prove the following:
`(x^("p"("q"-"r")))/(x^("q"("p"-"r"))) ÷ (x^"q"/x^"p")^"r"` = 1
