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Evaluate the following expressions.

(a) [tex]\log_6 6^8 =[/tex] □
(b) [tex]\log_3 27 =[/tex] □
(c) [tex]\log_5 3125 =[/tex] □
(d) [tex]\log_7 7^{15} =[/tex] □

Answer :

We can evaluate each logarithm by using the logarithm property that states:

[tex]$$
\log_b (b^x) = x.
$$[/tex]

Let's go through each part step-by-step.

(a) Evaluate [tex]$\log_6 6^8$[/tex].

Since the base of the logarithm is the same as the base of the exponent, we have:

[tex]$$
\log_6 6^8 = 8.
$$[/tex]

(b) Evaluate [tex]$\log_3 27$[/tex].

Notice that [tex]$27$[/tex] can be written as [tex]$3^3$[/tex], so:

[tex]$$
\log_3 27 = \log_3 (3^3) = 3.
$$[/tex]

(c) Evaluate [tex]$\log_5 3125$[/tex].

Similarly, [tex]$3125$[/tex] can be expressed as [tex]$5^5$[/tex], hence:

[tex]$$
\log_5 3125 = \log_5 (5^5) = 5.
$$[/tex]

(d) Evaluate [tex]$\log_7 7^{15}$[/tex].

Again, using the logarithm property:

[tex]$$
\log_7 7^{15} = 15.
$$[/tex]

Thus, the final answers are:

- (a) [tex]$\log_6 6^8 = 8$[/tex],
- (b) [tex]$\log_3 27 = 3$[/tex],
- (c) [tex]$\log_5 3125 = 5$[/tex], and
- (d) [tex]$\log_7 7^{15} = 15$[/tex].

Thanks for taking the time to read Evaluate the following expressions a tex log 6 6 8 tex b tex log 3 27 tex c tex log 5 3125 tex d tex. 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!

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