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2 votes
Explain how to solve 5 x−2

=8 using the change of base formula log b

y= logb
logy

. Include the solution for x in your answer. Round your answer to the nearest thousandth. ( 10 points)

User DvdG
by
7.7k points

2 Answers

6 votes

Final answer:

To solve the equation 5x - 2 = 8 using the change of base formula logb(y) = logb(x), you need to rewrite the equation in logarithmic form and solve for x. The solution for x is 2.

Step-by-step explanation:

To solve the equation 5x - 2 = 8 using the change of base formula logb(y) = logb(x), you need to rewrite the equation in logarithmic form.

First, we need to rearrange the equation and isolate the logarithm:

5x - 2 = 8

5x = 8 + 2

5x = 10

x = 10/5

x = 2

Therefore, the solution for x in the equation 5x - 2 = 8 is x = 2.

User Jamsesso
by
8.2k points
3 votes

Final answer:

To solve 5x - 2 = 8, isolate x using algebra and the change of base formula does not apply unless x is part of a logarithmic expression. If x is within a logarithm, the change of base can be used to convert logarithms to a common base like 10 or e for easier computation.

Step-by-step explanation:

To solve the equation 5x - 2 = 8 using the change of base formula for logarithms, you should first isolate x on one side of the equation. Using algebra, you add 2 to both sides and then divide by 5 to solve for x. However, the question seems to refer to the transformation of a logarithmic equation using the change of base formula, which is given as logb(y) = logc(y) / logc(b), where c is a new base of the logarithm. This formula allows you to change the base of a log from b to another base c, which is commonly 10 or e (the base of the natural logarithm).

In the context provided, let's assume we wanted to change the base of a logarithm from an arbitrary base b to 10. Then, the solution would involve taking the logarithm of both sides of the original equation in base 10:

log10(5x - 2) = log10(8)

From this point, you use the properties of logarithms to solve for x. If x were inside a logarithm, we could then apply the change of base formula. But since the equation 5x - 2 = 8 is not a logarithmic equation, the change of base formula is not applicable. In any case, once x is within a logarithmic expression and if required, you can use the change of base formula to convert it into a base that your calculator can handle.

User Tusharmath
by
7.8k points

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