Mathematics: When and how do you use logarithms to solve exponential equations? give an example of an exponential equation that does not require logarithms to solve it and example of a problem that does require logarithms to solve it.

When and how do you use logarithms to solve exponential

Ответ:

yassinesayedahmad1

13.03.2022

$\bf 5^{x+3}=\cfrac{1}{125}\implies 5^{x+3}=\cfrac{1}{5^3}\implies 5^{x+3}=5^{-3}
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\textit{because the bases are the same, the exponents must also be the same}
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x+3=-3\implies \boxed{x=-6}\\\\
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3^x=4^{2x}\implies log(3^x)=log(4^{2x})\implies xlog(3)=(2x)log(4)
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\cfrac{x}{2x}=\cfrac{log(4)}{log(3)}\implies \cfrac{1}{x}=\cfrac{log(4)}{log(3)}\implies \cfrac{log(3)}{log(4)}=x\implies \boxed{0.79248125\approx x}$

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Ответ:

konoisaa

07.06.2020

Mathematics

9514 1404 393

k = 15

Step-by-step explanation:

Look for the missing factors that make all of the factors of 60k be squares.

60 = 2² × 3 × 5

The factors 3 and 5 each have an odd exponent (1), so those two factors must be part of k.

60k = 2² × 3 × 5 × k

is a perfect square when ...

3 × 5 = k = 15

For k = 15, 60k = 900 = 30²

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When and how do you use logarithms to solve exponential equations? give an example of an exponential equation that does not require logarithms to solve it and example of a problem that does require logarithms to solve it.

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