How do you solve 2x+1=3x?

1 Answer
Feb 26, 2016

Convert to logarithmic form.

Explanation:

log2x+1=log3x

Simplify using the rule logan=nloga

(x+1)log2=xlog3

Distribute on the left side. Don't forget you cannot multiply directly a log with a non-log (e.g 2×log3log6but is equal to 2log3)

xlog2+log2=xlog3

Put the x's to one side of the equation.

log2=xlog3xlog2

log2=x(log3log2)

Simplify the right side of the equation further by using the rule logmlogn=log(mn)

log2=x(log(32))

log2log(32)=x

You will want to ask your teacher if he/she wants the answer in exact form or rounded off. Just make sure to check.

Practice exercises:

  1. Solve for x. Leave answers in exact form.

a) 23x=5x+1

b). 5x3=32x+1

Challenge problem

Find the value of x in 24x6=5×3x+7