Mathematics: What is 2 (log₃8+log₃z) - log₃(3⁴-7²) written as a single logarithm?

What is 2 (log₃8+log₃z) - log₃(3⁴-7²) written as

Ответ:

elysabrina6697

15.03.2022

Before we start solving this problem we need to make sure that all logarithms have same base. They do. Base is 3.

We start by solving first brackets. We will use the rule:
log a + log b = log (a*b)

$log_{3} 8 + log_{3} z = log_{3} (8z)$

Now we are left with:
$2log_{3} (8z)- log_{3} ( 3^{4} - 7^{2} )$

To get rid of 2 we will use rule:
$a* log_{b} c= log_{b} c^{a}$

$2log_{3} (8z)= log_{3} (8z)^{2}$

Now we are left with:
$log_{3} (8z)^{2}-log_{3} ( 3^{4} - 7^{2} )$

To solve this we will use rule:
$log a -logb = log \frac{a}{b}$

$log_{3} (8z)^{2}-log_{3} ( 3^{4} - 7^{2} )= log_{3} \frac{64 z^{2} }{3^{4} - 7^{2}} =log_{3} \frac{64 z^{2} }{32} =log_{3} 2z^{2}$

0,0(0 оценок)

Ответ:

allisongallion23

28.07.2020

Mathematics

Without the graph I can't find the rate of change.

0,0(0 оценок)

What is 2 (log₃8+log₃z) - log₃(3⁴-7²) written as a single logarithm?

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question