If 3x+1 = 9x-3, Find the Value of 21+X.

If 3^{x + 1} = 9^{x - 3}, find the value of 2^{1 + x}.

Sum

3^{x + 1} = 9^{x - 3}⇒ 3^xx 3 = ( 3² )^{x - 3}
⇒ 3^xx 3 = `3^(2x)/3^6`

⇒ `3^6 xx 3 = 3^(2x)/3^x `

⇒ `3^7 = 3^x`
⇒ x = 7
⇒ `2^( 1 + x ) = 2^( 1 + 7 ) = 2^8 = 256`

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Solving Exponential Equations

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Chapter 7: Indices (Exponents) - Exercise 7 (C) [Page 101]

Chapter 7 Indices (Exponents)
Exercise 7 (C) | Q 5 | Page 101

Solve : `[3^x]^2` : 3x = 9 : 1

Solve for x: `4^(x-1) × (0.5)^(3 - 2x) = (1/8)^-x`

If a^x = b^y = c^z and b² = ac, prove that: y = `[2xz]/[x + z]`

Simplify : `[ 3 xx 9^( n + 1 ) - 9 xx 3^(2n)]/[3 xx 3^(2n + 3) - 9^(n + 1 )]`

Evaluate the following:

`sqrt(1/4) + (0.01)^(-1/2) - (27)^(2/3)`

Solve for x:
2^2x+1= 8

Solve for x:
5^x2 : 5^x= 25 : 1

Show that : `(1)/(1 + "a"^("p"- "q")) + (1)/(1 + "a"^("q"- "p")`

If 2250 = 2^a. 3^b. 5^c, find a, b and c. Hence, calculate the value of 3^a x 2^-b x 5^-c.

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