PreCalculusEquations Worksheet 1
Solve by getting each side in terms of the same base. No calculators should be used on this part.
2^x = 64
x = 6
2^(x^2) = 512
x^2 = 9
x = ±3
5^(2x+1) = 125
2x + 1 = 3
x = 1
7^(x^2+x) = 49^-7
x^2 + x - 2 = 0
(x+2)(x-1) = 0
x = -2, 1
2^(-x) = 32
x = -5
9^x = 3
3^(2x) = 3
x = 1/2
9^x = 27
3^(2x) = 3^3
x = 3/2
(1/49)^x = 7
7^(-2x) = 7
-2x = 1
x = -1/2
3^x = 2
3x = 6
x = 2
2^(3x-3) = 2^(x+1)
3x - 3 = x + 1
2x = 4
x = 2
8^x = 2^7 * 4^9 * 2^2
2^(3x) = 2^(7+18+2)
3x = 25
x = 25/3
(8x)^(-1) = 64^(-1/3)
8x = 4
x = 1/2
8x^(-3) = 64
x^(-3) = 8
x = 1/2
(8x)^(-1) = 64^(-1/3)
8x = 4
x = 1/2
Convert each equation to an exponential equation. Solve by getting each side in terms of the same base. No calculators should be used on this section.
log_2(16) = y
16 = 2^y
y = 4
log_(1/3)(27) = y
27 = (1/3)^y
y = -3
log_(1/216)(x) = 3
x = (1/216)^3
log_b(125) = 3
125 = b^3
b = 5
log_(1/8)(2) = y
2 = (1/8)^y
y = -1/3
log_(3/2)(9/4) = y
9/4 = (3/2)^y
y = 2
log_b(81) = 4
81 = b^4
b = 3
log_b(1/27) = -3/2
1/27 = b^(-3/2)
b = 9
log_(sqrt(8))(1/8) = y
1/8 = (sqrt(8))^y
y = -2
log_(1000)(10) = y
10 = 1000^y
y = 1/3
log_9(x) = 1
x = 9^1
x = 9
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