Question

What is the value of x in 2(5^x)=15?

A). log 7 - log 5

B). log 2

C). log 5/log 7

D). log 7/log 5

Answer 1

`\displaystyle{x = (\log 7)/(\log 5)}`

Explanation:

Given the equation:

`\displaystyle{2\left(5^x\right)=14}`

Divide both sides by 2:

`\displaystyle{(2\left(5^x\right))/(2)=(14)/(2)}\\\\\displaystyle{5^x=7}`

Apply common logarithm both sides:

`\displaystyle{\log 5^x = \log 7}`

From the property:

`\displaystyle{\log a^n = n\log a}`

Thus:

`\displaystyle{x\log 5 = \log 7}`

Divide both sides by log5:

`\displaystyle{(x\log 5)/(\log 5) = (\log 7)/(\log 5)}\\\\\displaystyle{x = (\log 7)/(\log 5)}`