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scoray [572]
3 years ago
15

Use the Change of Base Formula to evaluate log3 58. Then convert log3 58 to a logarithm in base 4. Round to the nearest thousand

th.
Mathematics
2 answers:
boyakko [2]3 years ago
6 0

Answer:

\log_358\approx 3.696

\Rightarrow \dfrac{\log_458}{\log_43}

Step-by-step explanation:

Given: \log_358

We need to re-write the log expression with base 4 using base change property of log.

Log property:

\log_ab=\dfrac{\log_cb}{\log_ca}

Evaluate:

\Rightarrow \log_358

\Rightarrow \dfrac{\log58}{\log3}

\Rightarrow \dfrac{1.763427}{0.47712}\approx 3.696

Convert with base 4:

\Rightarrow \log_358

\Rightarrow \dfrac{\log_458}{\log_43}

Natali5045456 [20]3 years ago
5 0
Hello,

log_3(58)= \dfrac{ln(58)}{ln(3)}=3,69597450... \\

log_3(58)=log_4(x)\\

 \dfrac{ln(58)}{ln(3)} = \dfrac{ln(x)}{4}==\textgreater\ x=e^{ \frac{ln(58)*ln(4)}{ln(3)}}\\

 =167,957104437222249066099...



≈167.96
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Answer:

a) Sketch the graph of the function f. (it is in the attached file)

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For 2014 the ratio is 3.5

c) Over what years is the ratio constant?

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Step-by-step explanation:

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f(x)=-0.03t+4.25  for 5≤t<15

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So:

m=-0.03 for 5≤t<15

m=-0.075 for 15≤t≤35

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|-0.03| and |-0.075| or 0.03 and 0.075, easily finding that 0.075>0.03

And doing the sames process for the years in question (c):

t=15, 1995+15=2010, and t=35, 1995+35=2030

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