College

We appreciate your visit to Rewrite tex 2 x 128 tex as a logarithmic equation A tex log x 128 2 tex B tex log 2 x 128 tex C. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Rewrite [tex]$2^x = 128$[/tex] as a logarithmic equation.

A. [tex]\log_x 128 = 2[/tex]
B. [tex]\log_2 x = 128[/tex]
C. [tex]\log_2 128 = x[/tex]
D. [tex]\log_{128} x = 2[/tex]

Answer :

To rewrite the exponential equation

[tex]$$2^x = 128$$[/tex]

in logarithmic form, recall the definition of logarithms: if

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

then it can be rewritten as

[tex]$$\log_a c = b.$$[/tex]

Applying this to the equation [tex]$2^x = 128$[/tex], where [tex]$a=2$[/tex], [tex]$b=x$[/tex], and [tex]$c=128$[/tex], we get

[tex]$$\log_2 128 = x.$$[/tex]

To check, note that [tex]$128 = 2^7$[/tex], so indeed

[tex]$$\log_2 128 = 7,$$[/tex]

which confirms that [tex]$x = 7$[/tex].

Thus, the logarithmic form of the equation is

[tex]$$\log_{2} 128 = x.$$[/tex]

Thanks for taking the time to read Rewrite tex 2 x 128 tex as a logarithmic equation A tex log x 128 2 tex B tex log 2 x 128 tex C. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada