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Directions: Write each logarithmic equation in exponential form.
7. log, 49=2
4
10. logio 100,000 = 5
8.
109₂ 16
log₂
11. log4 1024 = 5
9.
log, 48 = x
12. log⁹ 729= 3

Directions Write each logarithmic equation in exponential form 7 log 492 4 10 logio 100000 5 8 109 16 log 11 log4 1024 5 9 log 48 x 12 log 729 3 class=

Respuesta :

leneveah143

Answer:

Step-by-step explanation:

1. To write the logarithmic equation "log base 4 of 49 equals 2" in exponential form, we need to remember that logarithms and exponentials are inverses of each other. In this case, the base of the logarithm is 4, the logarithm is 2, and the result is 49.

The exponential form of this equation is: 4² = 49.

2. To write the logarithmic equation "log base 10 of 100,000 equals 5" in exponential form, we can apply the same concept. The base of the logarithm is 10, the logarithm is 5, and the result is 100,000.

The exponential form of this equation is: 10⁵ = 100,000.

3. To write the logarithmic equation "log base 2 of 16 equals 9" in exponential form, we use the same approach. The base of the logarithm is 2, the logarithm is 9, and the result is 16.

The exponential form of this equation is: 2⁹ = 16.

4. To write the logarithmic equation "log base 4 of 1024 equals 5" in exponential form, we follow the same steps. The base of the logarithm is 4, the logarithm is 5, and the result is 1024.

The exponential form of this equation is: 4⁵ = 1024.

5. To write the logarithmic equation "log base 10 of 48 equals x" in exponential form, we can apply the same logic. The base of the logarithm is 10, the logarithm is x, and the result is 48.

The exponential form of this equation is: 10^x = 48.

6. To write the logarithmic equation "log base 9 of 729 equals 3" in exponential form, we use the same concept. The base of the logarithm is 9, the logarithm is 3, and the result is 729.

The exponential form of this equation is: 9³ = 729.

By converting logarithmic equations into exponential form, we can easily solve for the unknown values and better understand the relationship between logarithms and exponentials.

semsee45

Answer:

[tex]\textsf{7)}\quad 7^2=49[/tex]

[tex]\textsf{8)}\quad 2^{-4}=\dfrac{1}{16}[/tex]

[tex]\textsf{9)}\quad 8^x=48[/tex]

[tex]\textsf{10)}\quad 10^5=100000[/tex]

[tex]\textsf{11)}\quad 4^5=1024[/tex]

[tex]\textsf{12)}\quad 9^3=729[/tex]

Step-by-step explanation:

To write each logarithmic equation in exponential form, we can use the following rule:

[tex]\boxed{\begin{array}{c}\underline{\textsf{Logarithmic Rule}}\\\\\log_ab=c \iff a^c=b\end{array}}[/tex]

Therefore:

[tex]\textsf{7)}\quad \log_{7}49=2\implies \boxed{7^2=49}[/tex]

[tex]\textsf{8)}\quad \log_2\dfrac{1}{16}=-4\implies \boxed{2^{-4}=\dfrac{1}{16}}[/tex]

[tex]\textsf{9)}\quad \log_{8}48=x\implies \boxed{8^x=48}[/tex]

[tex]\textsf{10)}\quad \log_{10}100000=5\implies \boxed{10^5=100000}[/tex]

[tex]\textsf{11)}\quad \log_{4}1024=5\implies \boxed{4^5=1024}[/tex]

[tex]\textsf{12)}\quad \log_{9}729=3\implies \boxed{9^3=729}[/tex]

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