Let's solve the problem step by step.
We are given logarithmic expressions and need to convert them into
exponential form. The general rule for converting logarithmic form to exponential form is:
> If $ \log_b(a) = c $, then $ b^c = a $
This means:
- The
base of the logarithm becomes the
base of the exponent.
- The
result (the right-hand side of the equation) becomes the
exponent.
- The
argument of the log (the number inside the log) becomes the
result of the exponentiation.
---
Let's go through each one:
1.
$ \log_3 9 = 2 $
- Base: 3
- Result: 2
- Argument: 9
So, in exponential form:
$$
3^2 = 9
$$
2.
$ \log_4 64 = 3 $
- Base: 4
- Result: 3
- Argument: 64
Exponential form:
$$
4^3 = 64
$$
3.
$ \log_5 25 = 2 $
- Base: 5
- Result: 2
- Argument: 25
Exponential form:
$$
5^2 = 25
$$
4.
$ \log_2 128 = 7 $
- Base: 2
- Result: 7
- Argument: 128
Exponential form:
$$
2^7 = 128
$$
5.
$ \log_3 \left(\frac{1}{27}\right) = -3 $
- Base: 3
- Result: -3
- Argument: $ \frac{1}{27} $
Exponential form:
$$
3^{-3} = \frac{1}{27}
$$
6.
$ \log_6 36 = 2 $
- Base: 6
- Result: 2
- Argument: 36
Exponential form:
$$
6^2 = 36
$$
7.
$ \log_5 \left(\frac{1}{625}\right) = -4 $
- Base: 5
- Result: -4
- Argument: $ \frac{1}{625} $
Exponential form:
$$
5^{-4} = \frac{1}{625}
$$
---
Final Answer Table:
| Logarithmic Form | Exponent Form |
|------------------|----------------|
| $ \log_3 9 = 2 $ | $ 3^2 = 9 $ |
| $ \log_4 64 = 3 $ | $ 4^3 = 64 $ |
| $ \log_5 25 = 2 $ | $ 5^2 = 25 $ |
| $ \log_2 128 = 7 $ | $ 2^7 = 128 $ |
| $ \log_3 \left(\frac{1}{27}\right) = -3 $ | $ 3^{-3} = \frac{1}{27} $ |
| $ \log_6 36 = 2 $ | $ 6^2 = 36 $ |
| $ \log_5 \left(\frac{1}{625}\right) = -4 $ | $ 5^{-4} = \frac{1}{625} $ |
✔ All conversions follow the rule: $ \log_b(a) = c \Rightarrow b^c = a $
Let me know if you'd like this printed or formatted differently!
Parent Tip: Review the logic above to help your child master the concept of exponential and logarithmic equations worksheet.
