How do you solve $3^(x+2) = 10^(x-1)$ ?

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Answer 1 · 2018-07-13T13:36:35

I tried this:

I would take the logarithm in base $10$ (written $"L"og$ ) of both sides:

$"L"og(3^(x+2))="L"og(10^(x-1))$

use a property of log to manipulate the powers:

$(x+2)"L"og(3)=(x-1)"L"og(10)$

but $"L"og(10)=1$ so we get:

$(x+2)"L"og(3)=x-1$

rearrange:

$x"L"og(3)+2"L"og(3)-x=-1$

$x["L"og(3)-1]=-2"L"og(3)-1$

$x=(-2"L"og(3)-1)/["L"og(3)-1]=3.73746$

using a normal pocket calculator to evaluate the log in base $10$ .

How do you solve 3^(x+2) = 10^(x-1)3^(x+2) = 10^(x-1)?