Get Crazy with the logs

Algebra Level 1

log ⁡ x ( 34 ) = t , x > 0 \large \log_{x}(34) = t , x > 0

Which of the following mathematical equations is always true regarding the given equation above?

x 34 = 34 t \frac{x}{34} = 34t 3 4 x = t 34^x = t x t = 34 x^t = 34 34 x = t 34x = t

Karlie Puth by Karlie Puth , 20, Philippines

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3 solutions

Aditya Sky
Apr 9, 2016

You must specify in the question that x ≠ 1 \color{#D61F06}{x ≠ 1} .

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Karlie Puth
Apr 8, 2016

This problem is very simple, if you know your calculus...

The equation "logx (z) = y" simply means that x^y = z.

Use your calculator and enter this equation. log2 (32) = ? This can be translated into 2^x = 32, where x is the unknown variable or value. And so, the answer will be 5. (2^5 = 32).

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  • we know Logx to the base b can be written b to the power of y = x therefore x to the power of t = 34
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