2 years ago

When does a sequence and series become an arithmetic sequence and arithmetic series?

Mathematics

1 answer:

maria [59]2 years ago

4 0

Answer:

An arithmetic sequence is a sequence of numbers in which the difference between the consecutive terms is constant.

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Solve 4^x-5 = 6 for x using the change of base formula log base b of y equals log y over log b

Ronch [10]

Answer:

$4^x-5=6$ gives the solution $x=\frac{\log(11)}{\log(4)}$ .

$4^{x-5}=6$ gives the solution $x=\frac{\log(6)}{\log(4)}+5$ .

Step-by-step explanation:

I will solve both interpretations.

If we assume the equation is $4^{x}-5=6$ , then the following is the process:

$4^x-5=6$

Add 5 on both sides:

$4^x=6+5$

Simplify:

$4^x=11$

Now write an equivalent logarithm form:

$\log_4(11)=x$

$x=\log_4(11)$

Now using the change of base:

$x=\frac{\log(11)}{\log(4)}$ .

If we assume the equation is $4^{x-5}=6$ , then we use the following process:

$4^{x-5}=6$

Write an equivalent logarithm form:

$\log_4(6)=x-5$

$x-5=\log_4(6)$

Add 5 on both sides:

$x=\log_4(6)+5$

Use change of base formula:

$x=\frac{\log(6)}{\log(4)}+5$

6 0

3 years ago

When does a sequence and series become an arithmetic sequence and arithmetic series​?

When does a sequence and series become an arithmetic sequence and arithmetic series?