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If 6.9^a = 4.7^b, then b/a = ?

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If 6.9^a = 4.7^b, then b/a = ? Round the answer to two decimal places.

a*log(6.9) = b*log(4.7)

log(4.7)/log(6.9) = 0.80

Did I do this wrong? This dosn't seem to be the correct answer.

Jan 30, 2018

#1
+2338
+1

You are so incredibly close to the right answer. Let me see if I can steer you in the right direction, if I can.

$$6.9^a=4.7^b\\ \log\left(6.9^a\right)=\log\left(4.7^b\right)\\ a\log 6.9=b\log4.7\\ \frac{a}{b}=\frac{\log 4.7}{\log 6.9}\approx0.80$$

Your answer is wrong because you solved for something other than what the question asked for. The above is the work that you provided. In the above, you solved for $$\frac{a}{b}$$, but what is the question asking you to solve for? Adjust your solving so that you are solving for the correct expression.

Jan 30, 2018

#1
+2338
+1

You are so incredibly close to the right answer. Let me see if I can steer you in the right direction, if I can.

$$6.9^a=4.7^b\\ \log\left(6.9^a\right)=\log\left(4.7^b\right)\\ a\log 6.9=b\log4.7\\ \frac{a}{b}=\frac{\log 4.7}{\log 6.9}\approx0.80$$

Your answer is wrong because you solved for something other than what the question asked for. The above is the work that you provided. In the above, you solved for $$\frac{a}{b}$$, but what is the question asking you to solve for? Adjust your solving so that you are solving for the correct expression.

TheXSquaredFactor Jan 30, 2018