Rewrite the given equation in exponential format

6 answers
Question:

Rewrite the given equation in exponential format

[tex]Rewrite the given equation in exponential format[/tex]


Answers

 [tex]\bold{(20x)^{\frac{1}{12}}=(\frac{4}{5})^y}[/tex]

Step-by-step explanation:

[tex]log_{\frac{4}{5}}(20x)=12y\\\\\text{divide 12 from both sides:}\quad \frac{1}{12}log_{\frac{4}{5}}(20x)=y\\\\\text{condense log (coefficient converts to exponent):}\quad log_{\frac{4}{5}}(20x)^{\frac{1}{12}}=y\\\\\text{use log rules to convert log to exponential form:}\quad (20x)^{\frac{1}{12}}=(\frac{4}{5})^y[/tex]

[tex]10^{-6}=7[/tex]

Step-by-step explanation:

Remember that according to the laws of logarithms if [tex]log_ay=x[/tex], then [tex]a^x=y[/tex],

In other words to convert a logarithm to an exponential equation we just need to raise the base of the logarithm to the result and equate that to the argument of the logarithm.

Since our logarithm does not have a base, its base is 10; therefore [tex]a=10[/tex]. The argument of our logarithm is 7, so [tex]y=7[/tex]. The result of our logarithm is -6, so [tex]x=-6[/tex].

Replacing values

[tex]log_ay=x[/tex] ⇔ [tex]a^x=y[/tex]

[tex]log_{10}7=-6[/tex] ⇔ [tex]10^{-6}=7[/tex]

By the way [tex]log_{10}7=-6[/tex] is not a true equation since [tex]10^{-6}\neq 7[/tex].

[tex]10^{-6}=7[/tex]

Step-by-step explanation:

Remember that according to the laws of logarithms if [tex]log_ay=x[/tex], then [tex]a^x=y[/tex],

In other words to convert a logarithm to an exponential equation we just need to raise the base of the logarithm to the result and equate that to the argument of the logarithm.

Since our logarithm does not have a base, its base is 10; therefore [tex]a=10[/tex]. The argument of our logarithm is 7, so [tex]y=7[/tex]. The result of our logarithm is -6, so [tex]x=-6[/tex].

Replacing values

[tex]log_ay=x[/tex] ⇔ [tex]a^x=y[/tex]

[tex]log_{10}7=-6[/tex] ⇔ [tex]10^{-6}=7[/tex]

By the way [tex]log_{10}7=-6[/tex] is not a true equation since [tex]10^{-6}\neq 7[/tex].

For this case we have that by definition of logarithmic properties that, the expression

[tex]log_ {b} (a) = c[/tex] is equivalent to:

[tex]b ^ c = a[/tex]

Then, we have the following expression:

[tex]log_ {7} () = - 3[/tex]

It can be equivalent to:

[tex]7 ^ {- 3} =[/tex]

The correct option is option A

[tex]7 ^ {-3}[/tex]

growth because 'b' > 1 b decay because 'b' is < 1

In exponential form it is given as, 8⁻³ = [tex]$\frac{1}{512}[/tex]

Step-by-step explanation:

We have to write the given equation in the exponential form, that is in the form of base to the power value.

Given:

log₈ ([tex]$\frac{1}{512}[/tex]) = -3

Here the base is 8.

In the exponential form, it is written as,

base to the power 3 = 512

Here the reciprocal of 512 is given, so,

base to the power -3 =   [tex]$\frac{1}{512}[/tex]

So the exponential form is given as, 8⁻³ = [tex]$\frac{1}{512}[/tex]

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