Please help.
51. Solve:
125=(x3)/0.3^-3
a.7
b.14
c.15
d.9
53. 49x-2 = 7Ö 7
a.-5/4
b.5/4
c.11/4
d.-11/4
60. Simplify:
2log^3 6 - log^3 4
a.3
b.6
c.4
d.2
61. Solve the equation:
logb (x^2 + 7) = 2/3logb 64
a.9
b.3
c. √23
d. ±3
62. Solve:
(The fifth root of x) divided by 9, is equal to 7
no multiple answers available.
66. ln 1/√e
a. -√e
b.-1/2
c.1/e
d.1/2
67. Solve:
e3x = 8
a. In 5/ In 8
b. 3 In 8/ In 3
c. In 8/ 3
d. In 3/ 8
68. Solve:
1/ex = 7
a. In^1/7
b. In 1/7
c. In^7
d. In 7
69. Solve:
3e2x + 2 = 50
a. In 8
b.In 0.25
c.In 14
d. 0.5In 16
70. Solve:
|ln x| = 1
no multiple answers available.
71. Determine if the sequence is geometric, arithmetic, both, or neither: 256, 64, 16, 4, ...
a. Geometric
b. Arithmetic
c. Both
d. Neither
72. Determine if the sequence is arithmetic, geometric, both, or neither:
1/12, 2/13, 3/13, 4/14, ...
a. Geometric
b. Arithmetic
c. Both
d. Neither
73. Find the first four terms of the sequence:
tn = 2n + 1
a. 3; 5; 7; 9
b. 1; 3; 5; 7
c. 9; 11; 13; 15
d. 15; 17; 19; 21
74. Find the next two terms using the pattern in the difference between terms for the sequence:
24, 23, 21, 17, 9, ...
a. -7, -39
b. -3, -15
c. -11, -37
d. -2, -13
75. Find the next two terms using the pattern in the difference between terms for the sequence:
1, 2, 6, 15, 31, ...
a. 63, 127
b. 72, 114
c. 56, 92
d. 44, 73
76. Find the arithmetic mean for the pair of numbers:
2.3, 9.1
a. 10.47
b. 6.3
c. 5.7
d. 8.4
77. Choose a formula for the nth term of the sequence:
a^2/2, a^4/4, a^6/8, ...
a. a^2n/2^n
b. a^2n/2n
c. a^2n/2+n
d.2^n/a
78. A house purchased last year for $80,000 is now worth $96,000. Assuming that the value of the house continues to appreciate (increase) at the same rate each year, find the value 2 years from now.
no multiple answers available.
51. X^3/0.3^-3 = 125
0.3^3X^3 = 125
X^3 = 125/0.3^3
X^3 = 5^3/0.3^3
X = 5/0.3
X = 16.66666667.
67. e^3x = 8
3xLne = Ln8
3x*1 = Ln8
X = Ln8/3.
68. 1/e^x = 7
e^x = 1/7
x*Ln e = Ln 1/7
x*1 = Ln 1/7
X = Ln 1/7.
69. 3e2x+2 = 50
6ex = 48
X = 48/6e = 8/e = 2.943
70. |Ln x| = 1
Ln x = 1
X = e^1 = e = 2.7182.
78. Increase = 96000-80,000 = $16,000
%Increase = (16000/80000)*100%=20%/yr.
V = 80000(1+0.2)^3 = $138,240.
16 12 10 9 6 6
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----------------------
x=4
w=2
y=1
z=3
u=0
f=2
g=1
h=2
k=(3)---koken
ý=1
j=1
m=1
s=0
t=0
h=o
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To solve these questions, we'll go through each one step by step:
51. Solve: 125=(x3)/0.3^-3
To simplify, we can rewrite 0.3^-3 as 1/0.3^3. Now the equation becomes:
125 = (x^3)/(1/0.3^3)
Simplify further by multiplying both sides by 0.3^3:
125 * 0.3^3 = x^3
Now solve for x by taking the cube root of both sides:
x = cube root of (125 * 0.3^3)
Calculating this will give us the value of x.
53. 49x-2 = 7√7
To solve for x, we can first rewrite the square root as an exponent of 1/2:
49x-2 = 7^(1/2)
Next, we can simplify by taking the square root of both sides:
√(49x-2) = √7^(1/2)
Simplifying further:
7^(x-1) = 7^(1/2)
Since the bases are the same, we can equate the exponents:
x - 1 = 1/2
Solve for x by adding 1 to both sides:
x = 1/2 + 1
Calculate to find the value of x.
60. Simplify: 2log^3 6 - log^3 4
To simplify this expression, we need to apply the power rule of logarithms. The power rule states that log(a^b) = b * log(a).
Using this rule, we can rewrite the expression as:
2 * (log 6)^3 - (log 4)^3
Now, calculate the logarithms of 6 and 4, and raise them to the power of 3:
2 * (log 6)^3 - (log 4)^3 = 2 * (log6)^3 - (log4)^3
Calculate these values to get the final result.
61. Solve the equation: logb (x^2 + 7) = (2/3)logb 64
To solve this equation, we can use the power rule of logarithms again. The power rule states that log(a^b) = b * log(a).
Using this rule, we can rewrite the equation as:
logb(x^2 + 7) = (2/3) * logb 64
We know that logb 64 = 3, so the equation becomes:
logb(x^2 + 7) = (2/3) * 3
Simplify further:
logb(x^2 + 7) = 2
Now, convert the equation into exponential form:
b^2 = x^2 + 7
Solve for x by subtracting 7 from both sides, and then taking the square root of both sides:
x = square root of (b^2 - 7)
Calculate this to find the result.
62. Solve: (The fifth root of x) divided by 9, is equal to 7.
To solve this equation, we can translate it into an equation with the radical:
(x^(1/5))/9 = 7
Multiply both sides by 9:
x^(1/5) = 63
To get rid of the fifth root, raise both sides to the power of 5:
(x^(1/5))^5 = 63^5
Simplify further:
x = 63^5
Calculate this to find the value of x.
66. ln(1/√e)
To simplify this expression, we can use the properties of logarithms:
ln(1/√e) = ln(1) - ln(√e) = -ln(√e)
Now, simplify the logarithm:
ln(√e) = ln(e^(1/2)) = 1/2
The value of ln(1/√e) is 1/2.
Continue to next comment for the remaining questions.