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
Find x, if : 42x = `1/32`
Solve:
22x + 2x+2 − 4 × 23 = 0
If ax = by = cz and b2 = ac, prove that: y = `[2xz]/[x + z]`
Evaluate : `4/(216)^(-2/3) + 1/(256)^(-3/4) + 2/(243)^(-1/5)`
Evaluate the following:
`9^(5/2) - 3 xx 5^0 - (1/81)^((-1)/2)`
Evaluate the following:
`16^(3/4) + 2(1/2)^-1 xx 3^0`
Evaluate the following:
`sqrt(1/4) + (0.01)^(-1/2) - (27)^(2/3)`
Solve for x:
p3 x p-2 = px
If ax = by = cz and abc = 1, show that
`(1)/x + (1)/y + (1)/z` = 0.
Prove the following:
`root("ab")(x^"a"/x^"b")·root("bc")(x^"b"/x^"c")·root("ca")(x^"c"/x^"a")` = 1
