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Oliga [24]
4 years ago
12

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

Mathematics
1 answer:
ioda4 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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3 years ago
If Dave’s car gets 18 mi./gal. and gas costs $2.75/gal., then how much will it cost him to make a trip of 450 mi.?
grin007 [14]

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Step-by-step explanation:

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What is the sigma notation for this arithmetic series : 10+25+40+...+490+505
Lubov Fominskaja [6]

Answer:

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Step-by-step explanation:

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What we can notice is that the values are increasing by 15 units, therefore that will be the proportion that accompanies "n".

Now, we must calculate, how many times is "n", in the final value, for this we subtract the initial value, that is 10 and divide it by 15.

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7 0
3 years ago
Julia planet a rectangle garden that is 20 feet long she plays 56 feet of fencing around her Garten what is the width of her Gar
Aleksandr-060686 [28]

The width of rectangular garden(b) = 8 feet and

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Step-by-step explanation:

Given,

The length of rectangular garden(l) = 20 feet and

The perimeter of rectangular garden(fencing) = 56 feet

To find, the width of rectangular garden(b) = ? and

The area of rectangular garden = ?

We know that,

The area of rectangular garden = 2(l + b)

⇒  2(20 + b) = 56

⇒  20 + b = 28

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(3 - (-3)) / 2 = 3

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