Math  /  Algebra

QuestionSolve the equation for nn without using your calculator. Then use it to find the answer to the expression. 3n=95n+5=\begin{array}{l} 3^{n}=9 \\ 5 n+5=\square \end{array}

Studdy Solution

STEP 1

What is this asking? We need to figure out what power of 3 equals 9, and then use that value to solve 5n+55n + 5. Watch out! Don't mix up the order of operations!
We need to find nn *first*, and *then* plug it into 5n+55n + 5.

STEP 2

1. Find *n*
2. Calculate the expression

STEP 3

Alright, let's **rewrite** 9 as a power of 3!
We know that 33=93 \cdot 3 = 9, which means 32=93^2 = 9.

STEP 4

So, if 3n=93^n = 9 and 9=329 = 3^2, then we can say 3n=323^n = 3^2.
This means our **magical** nn is **2**!

STEP 5

Now, let's **substitute** our **newly discovered** n=2n = 2 into the expression 5n+55n + 5.

STEP 6

This gives us 52+55 \cdot 2 + 5.
Remember **PEMDAS/BODMAS**—we multiply *before* we add!

STEP 7

525 \cdot 2 gives us **10**.
So, we have 10+510 + 5.

STEP 8

Finally, 10+5=1510 + 5 = 15!
Our **final answer** for the expression is **15**!

STEP 9

n=2n = 2. 5n+5=155n + 5 = 15.

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