Question

Without using logarithm tables, find value of x in the equation:

log x³+ log5x =5log2-log⅖​

Answer 1

`x =2`

Explanation:

Given

`\log x\³+ \log5x =5\log2-\log(2)/(5)`

Required

Find x

We have:

`\log x\³+ \log5x =5\log2-\log(2)/(5)`

Apply exponent rule

`\log x\³+ \log5x =\log2^5-\log(2)/(5)`

`\log x\³+ \log5x =\log32 -\log(2)/(5)`

Apply product and quotient rules of logarithm

`\log (x\³* 5x) =\log(32 / (2)/(5))`

`\log (5x^4) =\log(80)`

Cancel log on both sides

`5x^4 = 80`

Divide by 5

`x^4 = 16`

Take 4th roots of both sides

`x =2`