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Oliga [24]
3 years ago
12

Verify each of the following by evaluating the logarithms. log10(103) + log10(104) = log10(107)

Mathematics
1 answer:
ioda3 years ago
7 0

Answer:

log₁₀(10³) + log₁₀(10⁴)

= log₁₀( 10³ × 10⁴ )

= log₁₀( 10³⁺⁴)

= log₁₀( 10⁷)

Step-by-step explanation:

Given:

log₁₀(10³) + log₁₀(10⁴) = log₁₀(10⁷)

Now,

we know the property of log function that

log(A) + log(B) = log(AB)

therefore,

applying the above property on the LHS, we get

log₁₀(10³) + log₁₀(10⁴) = log₁₀( 10³ × 10⁴ )

also,

xᵃ + xᵇ = xᵃ⁺ᵇ

therefore,

log₁₀( 10³ × 10⁴ ) = log₁₀( 10³⁺⁴)

= log₁₀( 10⁷)

Hence,

LHS = RHS

Hence proved

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ch4aika [34]

Answer:

Step-by-step explanation:

Th average rate of change is the slope of the secant line that goes through those 2 values of x.  Of course, each value of x also has a value of y.  The coordinates for these combinations of x's and y's are:

(-1, 5) and (4, 0).  We can use the slope formula to find the average rate of change of this function without having to know what the function's equation is:

m=\frac{0-5}{4-(-1)}=\frac{-5}{5}=-1

So the average rate of change, aka slope, between those 2 points is -1

7 0
3 years ago
What is 2/3 - 8/12 please help me understand this :)
ANEK [815]
You times the denominator from 2/3 by 4 so it can be equivalent to 8/12
2/3 x 4 = 8/12-8/12=0
3 0
3 years ago
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After substituting, what is the first step when evaluating 4y+9/7 when y=8
kenny6666 [7]

Answer:

  multiply 4 and 8 to get 32

Step-by-step explanation:

After substituting, the expression is ...

  4·8 +9/7

The order of operations tells you to do multiplication and division before addition and subtraction. You do them left-to-right. The multiplication on the left is 4·8, so you do that first. The result is ...

  32 + 9/7

Now, you can do the division:

  32 + (1 2/7)

And, finally, the addition:

  33 2/7

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Or, you could skip the division and go straight to adding a whole number and a fraction:

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7 0
3 years ago
The function f(x) = x2 has been translated 9 units up and 4 units to the right to form the function g(x). Which represents g(x)?
Inga [223]
For this case , the parent function is given by [tex f (x) =x^2
[\tex]
We apply the following transformations
Vertical translations :
Suppose that k > 0
To graph y=f(x)+k, move the graph of k units upwards
For k=9
We have
[tex]h(x)=x^2+9
[\tex]
Horizontal translation
Suppose that h>0
To graph y=f(x-h) , move the graph of h units to the right
For h=4 we have :
[tex ] g (x) =(x-4) ^ 2+9
[\tex]
Answer :
The function g(x) is given by
G(x) =(x-4)2 +9
8 0
3 years ago
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An equivalent expression for 12x+1 and 2(2x+5) please help​
zhannawk [14.2K]
<h2>Answer:</h2>

8x+9

<h2>Step-by-step explanation:</h2>

12x+1 = 2(2x+5)

<h3><em><u>Handle the brackets first</u></em></h3>

12x+1 = 4x+10

<h3><em><u>Collect like terms</u></em></h3>

=8x+9

3 0
3 years ago
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