Question

Explain how to solve 5x − 2 = 8 using the change of base formula log base b of y equals log y over log b. include the solution for x in your answer. round your answer to the nearest thousandth.

Answer 1

The correct answer is x = 3.29203

Logarithms change of base rule -

• The change of base formula is the formula that will give you the answer of a log with a different base by using only log calculations with a base of 10.
• The formula tells you to take the log of the number in parentheses and then divide it by the log of your base.

log 5x - 2) = log(8)

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

Log(5)=0.69897

log(8) = 0.80309

x - 2  = log(8) / log(5)

x - 2 = 1.29203

x = 2 + 1.29203

x = 3.29203

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