How do you solve log_3 (4x-5)=5?

3 Answers
Gió
Mar 15, 2018

I got x=62

Explanation:

Let us use the definition of log to write:

4x-5=3^5

rearrange:

4x=243+5

x=248/4=62

NB: definition of log
log_ba=x
so that:
a=b^x

Aviv S.
Mar 15, 2018

The solution is x=62.

Explanation:

Convert the equation to exponential form:

log_color(red)a(color(green)y)=color(blue)xqquadqquad<=>qquadqquadcolor(red)a^color(blue)x=color(green)y

Here's the actual equation:

color(white)=>log_color(red)3(color(green)(4x-5))=color(blue)5

=>color(red)3^color(blue)5=color(green)(4x-5)

color(white)=>243=4x-5

color(white)=>248=4x

color(white)=>62=x

color(white)=>x=62

That's the answer. Hope this helped!

Douglas K.
Mar 15, 2018

Given: log_3 (4x-5)=5

Make both sides the exponent of the base, 3:

3^(log_3 (4x-5))=3^5

The left side simplifies to the argument of the logarithm and the right side is computed with a calculator:

4x-5=243

Solve for x:

4x = 248

x = 62

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