Solving exponential and logarithmic equations: 3log6 (x+1)=9
i know i'm supposed to divide both sides by 3/log6 to get log(x+1)=3log6 (i think) but I'm not sure what i need to do next.

Question

Solving exponential and logarithmic equations: 3log6 (x+1)=9
i know i'm supposed to divide both sides by 3/log6 to get log(x+1)=3log6 (i think) but I'm not sure what i need to do next.

anonymous · Answer

the base is 6

mathmale · Answer

3log6 (x+1)=9
becomes $$\log_{6}(x+1)=3 $$

anonymous · Answer

@mathmale what happened to the 9?

mathmale · Answer

Use the left and right sides of this equation as the exponents of the base 6:$$6^{\log_{6}(x+1) }=6^3$$

mathmale · Answer

Dividing the original equation (both sides) by 3 reduces that 9 to a 3.

mathmale · Answer

Use the inverse property of the log and expo functions to simplify the above equation.

mathmale · Answer

Please note that $$10^{\log_{10}x }=x$$

mathmale · Answer

and follow that approach to tackle your math problem.

anonymous · Answer

ok so they should be equal when i'm finished?

mathmale · Answer

Please focus on the left side of your equation.  The base is 6.

Write the base 6 and then apply the given log to the base 6 of (x+1).  This whole expression boils down to what final result?

mathmale · Answer

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