solve each exponential equation. Given the value for x

Question

8^x=1/64
3^x=6
Can someone show me how to preform these. I would greatly appreciate it
Thank You

Answer 1

log ( a ^ n ) = n * log ( a )

log ( 1 / a ) = - log ( a )

log ( a * b ) = log ( a ) + log ( b )

64 = 8 * 8

log ( 64 ) = log ( 8 ) + log ( 8 )

log ( 64 ) = 2 * log ( 8 )

8 ^ x = 1 / 64

x * log ( 8 ) = log ( 1 / 64 )

x * log ( 8 ) = - log ( 8 * 8 )

x * log ( 8 ) = - [ log ( 8 ) +
log ( 8 ) ]

x * log ( 8 ) = - [ 2 * log ( 8 ) ]

x * log ( 8 ) = - 2 * log ( 8 ) Divide both sides by log ( 8 )

X = - 2

6 = 3 * 2

log ( 6 ) = log ( 3 ) + log ( 2 )

3 ^ x = 6

x * log ( 3 ) = log ( 6 )

x * log ( 3 ) = log ( 3 ) + log ( 2 ) Divide both sides by log ( 3 )

x = log ( 3 ) / log ( 3 ) + log ( 2 ) / log ( 3 )

x = 1 + log ( 2 ) / log ( 3 ) = 1.6309

Answer 2

Hi Bosnian,

I want thank you for working these problems out for me. I see how to work out the problems. You are great. I was getting so stressed, but now you have given me the faith that I can do this. I went back to school at an older age and algebra was taken when I was in 8th grade. Thank you for your time and I appreciate it so much

Answer 3

You're welcome.