Mathematics: : solve using logarithms. round the solution to the nearest hundredth. show your work. (you will need to use a calculator at some point)

: solve using logarithms. round the solution to

Ответ:

sophiat17

11.01.2022

To solve this problem we are going to use the power rule of logarithms: $ln(a^{x} )=xln(a)$ . Or in words: the logarithm of a power is the power times the logarithm of the base.
So, the first thing we are going to do is take natural logarithm,

, to both sides of our equation:
$ln(5^{x+2} )=ln(9^{2x+3} )$
Now, by the power rule of logarithms:
(x+2)ln(5)=(2x+3)ln(9)

$\frac{(x+2)ln(5)}{2x+3} =ln(9)$
$\frac{x+2}{2x+3}= \frac{ln(9)}{ln(5)}$
$\frac{x+2}{2x+3} =1.365$
x+2=1.365(2x+3)

$x=- \frac{2.095}{1.73}$
x=-1.211

Using our calculator we can conclude that

is approximately -1.211

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Ответ:

KennyMckormic

03.06.2023

Mathematics

The 7 in the number 94.087 represents 0.007 also known as the thousandths place in decimals.

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:
solve using logarithms. round the solution to the nearest hundredth. show your work.
(you will need to use a calculator at some point)

Ответ:

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