How do you solve #17^ { 4m + 6} + 8= 60#?

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Answer 1 · 2017-08-03T03:52:09

#m = -1.151#

We're asked to solve for #m# in the equation

#17^(4m+6) + 8 = 60#

Subtract #8# from both sides:

#17^(4m+6) = 52#

This can be expressed in logarithmic form as

#log_17(52) = 4m+6#

According to the change-of-base formula:

#log_17(52) = (log52)/(log17) ~~ ul(1.3946#

Therefore,

#1.3946 = 4m + 6#

Subtract #6# from both sides:

#-4.605 = 4m#

Divide both sides by #4#:

#color(blue)(ulbar(|stackrel(" ")(" "m = -1.151" ")|)#

#---------------------#

We can check this answer by plugging it back in to the original equation:

#17^(4(-1.151)+6) + 8 = 60#

#17^(4(-1.151)+6) ~~ ul(52.2#

#52.2 + 8 ~~ 60#