Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

log_(27)9=

$\log _{27} 9=$

View step-by-step help

View step-by-step help

Relationship between squares and square roots

Full solution

Q.

\log _{27} 9=

Find logarithm base and exponent: We need to find the value of $\log_{27}9$ . This means we are looking for the exponent that $27$ must be raised to in order to get $9$ .
Recognize powers of $3$ : Recognize that $27$ is a power of $3$ , specifically $27 = 3^3$ , and $9$ is also a power of $3$ , specifically $9 = 3^2$ .
Rewrite logarithm in base $3$ : Rewrite the logarithm in terms of the base $3$ : $\log_{3^3}(3^2)$ .
Apply logarithm property: Use the property of logarithms that says $\log_{a^c}(b^d) = \frac{d}{c} \cdot \log_a(b)$ . In this case, $\log_{3^3}(3^2) = \frac{2}{3} \cdot \log_3(3)$ .
Evaluate logarithm: Since $\log_3(3)$ is equal to $1$ (because $3$ raised to the power of $1$ is $3$ ), we have $\frac{2}{3} \times 1 = \frac{2}{3}$ .
Final result: Therefore, $\log_{27}9 = \frac{2}{3}$ .

More problems from Relationship between squares and square roots

Question

Solve the following equation for

y

\newline

\begin{array}{l} y+6=\sqrt{2 y^{2}+72} \\ y=\square \end{array}

Posted 3 months ago

Question

z=12.1+29 i

\newline

What is the real part of

z

\newline

What is the imaginary part of

z

Posted 3 months ago

Question

z=-400 i-44.5

\newline

What is the real part of

z

\newline

What is the imaginary part of

z

Posted 3 months ago

Question

z=-91+14.6 i

\newline

What is the real part of

z

\newline

What is the imaginary part of

z

Posted 3 months ago

Question

z=44 i+23.3

\newline

What is the real part of

z

\newline

What is the imaginary part of

z

Posted 3 months ago

Question

\log _{16} 8=

Posted 3 months ago

Question

\log _{5} 25=

Posted 3 months ago

Question

\log _{49} 7=

Posted 3 months ago

Question

\log _{3} 27=

Posted 3 months ago

Question

\log _{7} 49=

Posted 3 months ago