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Chapter 13: Problem 11

Write as the sum or difference of logarithms and simplify, if possible. Assume all variables represent positive real numbers. $$\log _{7} 5 d$$

Short Answer

Expert verified
The simplified expression is \(\log_7(5) + \log_7(d)\).

Step by step solution

01

Identify the given expression and apply the product rule

The given expression is: \(\log_7(5d)\). Since 5d is a product of two numbers, we can apply the product rule for logarithms and rewrite the expression as the sum of logarithms.
02

Apply the product rule

According to the product rule for logarithms, we can rewrite the given expression as the sum of the logarithms of the factors: \[\log_7(5d) = \log_7(5) + \log_7(d)\]
03

Simplify the expression (if possible)

In this case, there is no further simplification because the logarithms cannot be combined and no numerical values can be reduced. Hence, the final expression is: \[\log_7(5) + \log_7(d)\]

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Most popular questions from this chapter

Write as a single logarithm. Assume the variables are defined so that the variable expressions are positive and so that the bases are positive real numbers not equal to \(1 .\) $$\frac{1}{2} \log _{b}(c+4)-2 \log _{b}(c+3)$$

Find the inverse of each one-to-one function. $$h(x)=-\frac{3}{2} x+4$$

Solve equation. \(\log _{4} k+\log _{4}(k-6)=2\)

Find the inverse of each one-to-one function. $$g(x)=-4 x+8$$

Determine whether each function is one-to-one. If it is one-to-one, find its inverse. $$f=\\{(-4,3),(-2,-3),(2,-3),(6,13)\\}$$
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