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fredd [130]
3 years ago
11

A teacher used the change of base formula to determine whether the equation below is correct.

Mathematics
2 answers:
Mademuasel [1]3 years ago
6 0

Answer:

The equation is correct

Step-by-step explanation:

The equation, written as:

[log_2 (10)][log_4 (8)][log_10 (4)] = 3

Consider the change of base formula:

log_a (x) = [log_10 (x)]/ [log_10 (a)]

Applying the change of base formula to change the expressions in base 2 and base 4 to base 10.

(1)

log_2 (10) = [log_10 (10)]/[log_10 (2)]

= 1/[log_10 (2)]

(Because log_10 (10) = 1)

(2)

log_4 (8)  = [log_10 (8)]/[log_10 (4)]

Now putting the values of these new logs in base 10 into the left-hand side of original equation to verify if we have 3, we have:

[log_10 (2)][log_8 (4)][log_10 (4)]

= [1/ log_10 (2)][log_10 (8) / log_10 (4)][log_10 (4)]

= [1/log_10 (2)] [log_10 (8)]

= [log_10 (8)]/[log_10 (2)]

= [log_10 (2³)]/[log_10 (2)]

Since log_b (a^x) = xlog_b (a)

= 3[log_10 (2)]/[log_10 (2)]

= 3 as required

Therefore, the left hand side of the equation is equal to the right hand side of the equation.

Amiraneli [1.4K]3 years ago
5 0

Answer:

B on E2020.

Step-by-step explanation:

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Answer:

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3 0
2 years ago
Find three consecutive even integers such that the sum of the first, twice the second, three times the third is -76. What is the
ss7ja [257]

Answer:

The numbers are -14,-13 and -12

Step-by-step explanation:

<u><em>The correct question is </em></u>

Find three consecutive integers such that the sum of the first, twice the second and three times the third is -76. What is the number?

Let

x ----> the first consecutive integer

x+1 ---> the second consecutive integer

x+2 ---> the third consecutive integer

we have that

x+2(x+1)+3(x+2)=-76

solve for x

apply distributive property

x+2x+2+3x+6=-76

Combine like terms

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subtract 8 both sides

6x=-76-8

6x=-84

Divide by 6 both sides

x=-14

so

x+1=-14+1=-13

x+2=-14+2=-12

therefore

The numbers are -14,-13 and -12

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