Given the information below, answer the following "log" problems.

Question

Solve for x 

12 log 12= 3x log 3 + 2x log 8

 

3. If log ab +log bc +log ac =10 (for positive values of a,b,c) What is the value of log abc?

Answer 1

assume base 10

12log12=3xlog3+2xlog8

log12¹²=xlog3³+xlog8²

log12¹²=x(log27+log64)

log12¹²=x(log(27*64))

log12¹²=log(27*64)^x

12¹²=(27*64)^x

12¹²=(3*3*3*2*2*2*2*2*2)^x

12¹²=(12³)^x

12¹²=12^3x

12=3x

x=4

 

logab+logbc+logac=10

log(ab*bc*ac)=10

log(a²b²c²)=10

assume base10

log(10)(a²b²c²)=10

10¹⁰=a²b²c²

√10¹⁰=√a²b²c²

10⁵=abc

log(10)10⁵=log(10)abc

5log(10)10=log(10)abc

5*1=log(10)abc

5=log(10)abc